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Answers posted by meena.p

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By using the properties of definite integrals,evaluate the integral $ \begin{align*}\int\limits_0^\frac{\pi}{4} log (1+\tan x)\;dx \end{align*}$
answered Feb 13, 2013
Toolbox: (i)$ \int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int \limits_0^a f(x)dx=\int \...
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By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^1x\;(1-x)^n\;dx \end{align*}$
answered Feb 13, 2013
Toolbox: (i)$ \int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int \limits_0^a f(x)dx=\int \limits_0^a...
0 votes
By using the properties of definite integrals,evaluate the integral\[\int\limits_2^8\mid x-5 \mid\;dx\]
answered Feb 13, 2013
Toolbox: $ \int \limits_a^bf(x)dx=F(b)-F(a)$ $\int \limits_a^cf(x)dx=\int \limits_a^...
0 votes
By using the properties of definite integrals,evaluate the integral\[\int\limits_{-5}^5\mid x+2 \mid\;dx\]
answered Feb 13, 2013
Toolbox: $ \int \limits_a^bf(x)dx=F(b)-F(a)$ $ f(x)=|x+a|=f(x)= \left\{ \begin{array}{1 1} x+a...
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By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\pi}{2}\frac{\cos^5x\;dx}{\sin^5x+\cos^5x}\]
answered Feb 13, 2013
Toolbox: (i)$\int\limits_0^af(x)dx=\int\limits_0^af(a-x)dx$ (ii)$\sin(\frac{\pi}{2}-...
0 votes
By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\pi}{2}\frac{\sin^\frac{3}{2}\;x\;dx}{\sin^\frac{3}{2}\;x+\cos^\frac{3}{2}\;x}\]
answered Feb 13, 2013
Toolbox: (i)$\int\limits_0^af(x)dx=\int\limits_0^af(a-x)dx$ (ii)$\sin(\frac{\pi}{2}-...
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Choose the correct answer If f(x)=$\int\limits_0^x t\sin t\;dt,$ then f'(x) is
answered Feb 13, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$ \int udv=uv-\int vdu$ (i...
0 votes
Choose the correct answer in the value of the integral$\begin{align*}\int\limits_\frac{1}{3}^1\frac{(x-x^3)^\frac{1}{3}}{x^4}dx \end{align*}$ is
answered Feb 13, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\frac{d}{dx}(\cot x)=- cosec ^2 x$ (ii...
0 votes
By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\frac{\Large \pi}{\Large 2}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\;dx\]
answered Feb 13, 2013
Toolbox: (i)$\int \limits_0^a f(x)dx=\int \limits_0^a f(a-x)dx$ (ii)$\sin (\frac{\pi}{2}-x)=\c...
0 votes
By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_0^\frac{\Large \pi}{\Large 2}\cos^2x\;dx \end{align*}$
answered Feb 13, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\sin ^2x+\cos ^2x=1$ Gi...
0 votes
Evaluate the integral using substitution $\displaystyle\int\limits_1^2\bigg(\frac{1}{x}-\frac{1}{2x^2}\bigg)e^{2x}dx$
answered Feb 13, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int e^x[f(x)+f'(x)]dx=e^xf(x)+...
0 votes
Evaluate the integral using substitution\[\int\limits_{-1}^1\frac{dx}{x^2+2x+5}\]
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int \frac{dx}{x^2+a^2}=\frac{1...
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Evaluate the integral using substitution\[\int\limits_0^2\frac{dx}{x+4-x^2}\]
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ $\int \frac{dx}{a^2-x^2}=\frac{1}{2a...
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Evaluate the integral using substitution\[\int\limits_0^\frac{\large \pi}{2}\frac{\sin x}{1+\cos^2x}dx\]
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ Method of substitution:If $I=\int f(...
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Evaluate the integral using substitution $\begin{align*}\int\limits_0^1\sin^{-1}\bigg(\frac{2x}{1+x^2}\bigg)dx \end{align*}$
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-f(a)$ Method of integration by parts ...
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Evaluate the integral using substitution\[\int\limits_0^1\frac{x}{x^2+1}dx\]
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-f(a)$ (ii)$\int f(x)dx,if f(x)=t\;then f'(...
0 votes
Choose the correct answer in $\int\limits_0^\frac{2}{3}\frac{dx}{4+9x^2}$ equals
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-f(a)$ (ii)$\int \large\frac{dx}{x^2+a^2}=\...
0 votes
Choose the correct answer in $\int\limits_1^\sqrt 3\frac{dx}{1+x^2}\;equals$\[(A)\;\frac{\pi}{3}\qquad(B)\;\frac{2\pi}{3}\qquad(C)\;\frac{\pi}{6}\qquad(D)\;\frac{\pi}{12}\]
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-f(a)$ (ii)$\int \large\frac{dx}{x^2+a^2}=\...
0 votes
Evaluate the definite integral $\displaystyle\int\limits_0^1(xe^x+\sin\frac{\pi\;x}{4})dx$
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-f(a)$ (ii) Methods of integration by parts...
0 votes
Evaluate the definite integral $\displaystyle\int\limits_0^2\frac{6x+3}{x^2+4}dx$
answered Feb 12, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$ \int \large\frac{1}{x^2+a^2}dx...
0 votes
Evaluate the definite integral $\int\limits_0^\pi(\sin^2\frac{x}{2}-\cos^2\frac{x}{2})dx$
answered Feb 11, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int \cos x dx=\sin x+c$ ...
0 votes
Evaluate the definite integral\[\int\limits_0^\frac{\large\pi}{4}(2\sec^2x+x^3+2)dx\]
answered Feb 11, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int \sec^2xdx=\tan x$ ...
0 votes
Evaluate the definite integral $\displaystyle\int\limits_1^2\frac{5x^2}{x^2+4x+3}$
answered Feb 11, 2013
Toolbox: (i)$\int \limits_a^bf(x)dx=F(b)-F(a)$ (ii)If the given rational function is...
0 votes
Evaluate the definite integral\[\int\limits_0^1x\;e^{x^2}dx\]
answered Feb 11, 2013
Toolbox: (i)$ \int \limits_a^bf(x)dx=F(b)-F(a)$ (ii)If there are two functions u and...
0 votes
Evaluate the definite integral $\begin{align*}\int\limits_0^1\frac{2x+3}{5x^2+1}dx \end{align*}$
answered Feb 11, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)$\int \frac{1}{1+x^2}dx=\tan^{-1}+c$ (i...
0 votes
Evaluate the definite integral $\begin{align*}\int\limits_2^3\frac{xdx}{x^2+1} \end{align*}$
answered Feb 11, 2013
Toolbox: (i)$\int \limits_a^b f(x)dx=F(b)-F(a)$ (ii)Methods of substitution:$ \int f(x)dx.\; L...
0 votes
Evaluate the definite integral $\begin{align*}\int\limits_0^\frac{\Large \pi}{2}\cos^2xdx \end{align*}$
answered Feb 11, 2013
Toolbox: (i)∫abf(x)dx=F(b)−F(a)" role="presentation" style="position: relat...
0 votes
Evaluate the definite integral\[\int\limits_2^3\frac{dx}{x^2-1}\]
answered Feb 11, 2013
Toolbox: $\int \limits_a^b f(x)dx=F(b)-F(a)$ $\int \large \frac{dx}{x^2-a^2}=\frac{1...
0 votes
Evaluate the definite integral\[\int\limits_0^1\frac{dx}{1+x^2}\]
answered Feb 11, 2013
Toolbox: $\int \limits_a^b f(x)dx=F(b)-F(a)$ $\int\large\frac{dx}{1+x^2} dx=\tan^{-1...
0 votes
Evaluate the definite integral\[\int\limits_0^1\frac{dx}{\sqrt{1-x^2}}\]
answered Feb 11, 2013
Toolbox: $\int \limits_a^b f(x)dx=F(b)-F(a)$ $\int \large\frac{dx}{\sqrt{1-x^2}}=\si...
0 votes
Evaluate the definite integral\[\int\limits_\frac{\Large \pi}{\Large 6}^\frac{\Large \pi}{\Large 4}cosec x\;dx\]
answered Feb 10, 2013
Toolbox: $ \int \limits_a^b f(x)dx=F(b)- F(a)$ (ii)$\int cosec x dx= log |cosec x- \...
0 votes
Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\tan x\;dx\]
answered Feb 10, 2013
Toolbox: (i)$ \int \limits_a^b f(x)dx=F(b)- F(a)$ (ii)$\int \tan x dx= -log |\cos x|...
0 votes
Evaluate the definite integral\[\int\limits_4^5e^x\;dx\]
answered Feb 10, 2013
Toolbox: $ \int \limits_a^b f(x)dx=F(b)- F(a)$ (i)$\int e^xdx=e^x+c$ Given $...
0 votes
Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 2}\cos 2x\;dx\]
answered Feb 10, 2013
Toolbox: (i)$ \int \limits_a^b f(x)dx=F(b)- F(a)$ (ii)$\int \cos ax dx=-\frac{1}{a} ...
0 votes
Evaluate the definite integral\[\int\limits_0^\frac{\Large \pi}{\Large 4}\sin 2x\;dx\]
answered Feb 10, 2013
Toolbox: (i)$ \int \limits_a^b f(x)dx=F(b)- F(a)$ (ii)$\int \sin ax=-\frac{1}{a} \co...
0 votes
Evaluate the definite integral\[\int\limits_1^2(4x^3-5x^2+6x+9)\;dx\]
answered Feb 10, 2013
Toolbox: $\int \limits_a^b f(x)dx=F(b)-F(a)$ $\int x^ndx=\Large\frac{x^{n+1}}{n+1}$ ...
0 votes
Evaluate the definite integral\[\int\limits_2^3\frac{1}{x}dx\]
answered Feb 10, 2013
Toolbox: (i)$\int\limits_a^b f(x)dx= F(b)-F(a)$ (ii)$\int \frac{1}{x}dx=log x$ ...
0 votes
Evaluate the definite integral\[\int\limits_{-1}^1(x+1)dx\]
answered Feb 10, 2013
Toolbox: $\int\limits_a^b f(x)dx= F(b)-F(a)$ $ \int x^ndx=\Large\frac{x^{n+1}}{n+1}+...
0 votes
Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$
answered Feb 10, 2013
Toolbox:$\int\limits_a^b f(x)dx=\displaystyle\lim_{h \to 0}h[f(a)+f(a+h)+...f(a+(n-1)h]$ where $ ...
0 votes
Evaluate the definite integral as limits of sums\[\int\limits_{-1}^1e^xdx\]
answered Feb 9, 2013
Toolbox: $\int \limits_a^b f(x)dx=\lim_ {h \to 0} h[f(a)+f(a+h)+.....f(a+(n-1)h]$ Wh...
0 votes
Evaluate the definite integral as limits of sums\[\int\limits_1^4(x^2-x)dx\]
answered Feb 8, 2013
Toolbox: $\int\limits_a^b f(x)dx=lim_{h->0}h[f(a)+f(a+h)+...f(a+(n-1)h)]$ where $...
0 votes
Evaluate the definite integral as limits of sums $\begin{align*}\int\limits_2^3x^2dx \end{align*}$
answered Feb 8, 2013
Toolbox:$\int\limits_a^b f(x)dx=\displaystyle\lim_{h \to 0}h[f(a)+f(a+h)+...f(a+(n-1)h)]\;where\;h=\...
0 votes
Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^5(x+1)dx$
answered Feb 8, 2013
Toolbox:$\int\limits_a^b f(x)dx=\displaystyle\lim_{h \to 0}h[f(a)+f(a+h)+...f(a+(n-1)h)]\;where\;h=\...
0 votes
Evaluate the definite integral as limits of sums $\displaystyle\int\limits_a^bx\;dx$
answered Feb 8, 2013
Toolbox:$\int\limits_a^b f(x)dx=\displaystyle\lim_{h \to 0}[f(a)+f(a+h)+...f(a+(n-1))]\;when\;h=\fra...
0 votes
Choose the correct answer in $ \Large \int \normalsize \sqrt{x^2-8x+7} \: dx$ is equal to\[ \begin{array}{l} (A)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}+9\;log\mid x-4+\sqrt{x^2-8x+7}\mid + \; C \\ (B)\frac{1}{2}(x+4)\sqrt{x^2-8x+7}+9\;log\mid x+4+\sqrt{x^2-8x+7}\mid + \; C \\ (C) \frac{1}{2}(x-4)\sqrt{x^2-8x+7}-3\sqrt2log\mid x-4+\sqrt{x^2-8x+7}\mid+ \; C \\ (D)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}-\frac{9}{2}\;log\mid x-4+\sqrt{x^2-8x+7}\mid + \; C \end{array}\]
answered Feb 8, 2013
Toolbox: $\int \sqrt{x^2-a^2}dx=\frac{x}{2}\sqrt{x^2-a^2}-\frac {a^2}{2}log |x+\sqrt{x^2-a...
0 votes
Choose the correct answer in $\Large \int \normalsize \sqrt{1+x^2}dx$ is equal to \[\begin{array}{l}(A)\;\frac{x}{2}\sqrt{1+x^2}+\frac{1}{2}log\LARGE\mid\normalsize\bigg(x+\sqrt{1+x^2}\bigg)\LARGE\mid\normalsize+C \\(B)\;\frac{2}{3}(1+x^2)^\frac{3}{2}+C\qquad \\ (C)\;\frac{2}{3}x(1+x^2)^\frac{3}{2}+ C \\ (D)\;\frac{x^2}{2}\sqrt{1+x^2}+\frac{1}{2}x^2log\LARGE\mid\normalsize x+\sqrt{1+x^2}\LARGE\mid\normalsize+C \end{array}\]
answered Feb 8, 2013
Toolbox: $\int \sqrt{a^2+x^2}dx=\frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}log |x+\sqrt{x^2+a^...
0 votes
Integrate the function\[\sqrt{1+\frac{x^2}{9}}\]
answered Feb 8, 2013
Toolbox: $\int \sqrt{x^2+a^2}dx=\frac{x}{2}\sqrt{x^2+a^2}+\frac {a^2}{2}log |x+\sqrt{x^2+a...
0 votes
Integrate the function $\sqrt{x^2+3x}$
answered Feb 8, 2013
Toolbox: ∫x2−a2dx=x2x2−a2+a22log|x+x2−a2|+c" role="pr...
0 votes
Integrate the function $\sqrt{1+3x-x^2}$
answered Feb 7, 2013
Toolbox: $\int \sqrt{a^2-x^2}dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac {a^2}{2}\sin^{-1}(\frac{x}{a})+c$...
0 votes
Integrate the function $\sqrt{x^2+4x-5}$
answered Feb 7, 2013
Toolbox: $\int \sqrt{x^2-a^2}dx=\frac{x}{2}\sqrt{x^2-a^2}+\frac {a^2}{2}log |x+\sqrt{x^2-a^2}|+c$...
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