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Compute the area of the bounded by the line $x+2y=2,y-x=1$ and $2x+y=7.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Draw a rough sketch of the region {(x,y):$y^2\leq 6ax $ and $x^2+y^2\leq 16a^2$}.Also find the area of the region sketched using method of integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of region bounded by the triangle whose vertices are $(-1,1),(0,5)$ and $(3,2)$ using integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area bounded by the curve y=sinx between $x=0$ and $x=2\pi$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y^2=2x$ and $x^2+y^2=4x.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area bounded by the curve $y=\sqrt x,x=2y+3$ in the first quadrant and $x$-axis.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the enclosed by the curve $y=-x^2$ and the straight line $x+y+2=0.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by $y=\sqrt x$ and $y=x.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Determine the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Draw a rough sketch of the curve $y=\sqrt{x-1}$ in the interval [1,5].Find the area under the curve and between the lines $x=1$ and $x=5$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Using integration,find the area of the region bounded by the line $2y=5x+7,x$-axis and the lines $x=2$ and $x=8.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Calculate the area under the curve $y=2\sqrt x$ included between the lines $x=0$ and $x=1$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Sketch the region $\{(x,0):y=\sqrt {4-x^2}$} and $x$-axis.Find the area of the region using integration.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the line $x=2$ and the parabola $y^2=8x$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region enclosed by the parabola $x^2=y$ and the line $y=x+2$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region included between $y^2=9x$ and $y=x$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y^2=4x,x^2=4y$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curve $y=x^3$ and $y=x+6$ and $x=0$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the parabola $y^2=2px,x^2=2py.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the curves $y^2=9x,y=3x.$

asked Jan 15, 2013 by sreemathi.v

1 answer

The value of $\large\int\limits_{-\pi}^\pi$$\sin^3x\cos^2x dx$ is___________.

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large\int\frac{\sin x}{3+4\cos^2x}$$dx$=___________.

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\Large \int\frac{1}{1+4x^2}$$dx=\large\frac{\pi}{8},$then a=____________.

asked Jan 15, 2013 by sreemathi.v

1 answer

$\int\Large{\frac{x+3}{(x+4)^2}}\normalsize e^xdx$=___________.

asked Jan 15, 2013 by sreemathi.v

1 answer

$\int\limits_0^{\Large\frac{\pi}{2}}\cos x\;e^{\sin x} dx$ is equal to ____________.

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\limits_0^\frac{\pi}{2}\normalsize \sqrt {1-\sin2x}\;dx$ is equal to $(A)\;0\quad(B)\;2\quad(C)\;1\quad(D)\;-1$

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\limits_\frac{-\pi}{4}^\frac{\pi}{4}\frac{dx}{1+\cos2x}$ is equal to $(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;4$

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\large \frac{x^3dx}{\sqrt{1-x^2}}=\normalsize a(1-x^2)^{\Large\frac{3}{2}}+b\sqrt{1-x^2}+C$,then

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x+\sin x}{1+\cos x}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;\log\mid1+\cos x\mid+C & (B)\;\log\mid x+\sin x\mid+C\\(C)\;x-\tan\frac{x}{2}+C & (D)\;x\;\tan\frac{x}{2}+C \end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x^3}{x+1}$ is equal to\begin{array}{1 1}(A)\;x+\frac{x^2}{2}+\frac{x^3}{3}-log\mid1-x\mid+C & (B)\;x+\frac{x^2}{2}-\frac{x^3}{3}-log\mid1-x\mid+C\\(C)\;x-\frac{x^2}{2}-\frac{x^3}{3}-log\mid1+x \mid+C & (D)\;x-\frac{x^2}{2}+\frac{x^3}{3}-log\mid1+x \mid+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

If $\Large \int\frac{dx}{(x+2)(x^2+1)}=\normalsize a\log\mid 1+x^2\mid+b\tan^{-1}x+\frac{1}{5}\log\mid x+2\mid+C$,then\begin{array}{1 1}(A)\;a=\frac{-1}{10},b=\frac{-2}{5} & (B)\;a=\frac{1}{10},b=\frac{-2}{5}\\(C)\;a=\frac{-1}{10},b=\frac{2}{5} & (D)\;a=\frac{1}{10},b=\frac{2}{5}\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{x^9}{(4x^2+1)^6}\normalsize dx $ is equal to\begin{array}{1 1}(A)\;\frac{1}{5x}\bigg(4+\frac{1}{x^2}\bigg)^{-5}+C & (B)\;\frac{1}{5}\bigg(4+\frac{1}{x^2}\bigg)^{-5}+C\\(C)\;\frac{1}{10x}(1+4)^{-5}+C & (D)\;\frac{1}{10}\bigg(\frac{1}{x^2}+4\bigg)^{-5}+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int e^x\bigg(\frac{1-x}{1+x^2}\bigg)^2 \normalsize dx$ is equal to

asked Jan 15, 2013 by sreemathi.v

1 answer

$ \int\tan^{-1}\sqrt x$ is equal to which of the following options:

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{dx}{\sin(x-a)\sin(x-b)}$ is equal to\begin{array}{1 1}(A)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C & (B)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \\(C)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C &(D)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

$\Large \int\frac{\cos 2x-\cos 2\theta}{\cos x-\cos\theta}\normalsize dx$ is equal to\begin{array}{1 1}(A)\;2(\sin x+x\cos\theta)+C & (B)\;2(\sin x-x\cos\theta)+C\\(C)\;2(\sin x+2x\cos\theta)+C & (D)\;2(\sin x-2x\cos\theta)+C\end{array}

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_ {\Large\frac{-\pi}{4}}^{\Large\frac{\pi}{4}} \log(\sin x+\cos x)dx$

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_0^{\Large \pi} x \log \sin xdx$

asked Jan 15, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^1 x\;log(1+2x)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_0^{\Large\frac{\pi}{2}}\large\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}\quad\normalsize \text{(Hint:Divide Numerator and Denominator by $\cos^4x)$}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate :$\int \sqrt \tan x \;dx\;$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int e^{-3x}\cos^3xdx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_{\Large \frac{\pi}{3}}^{\Large \frac{\pi}{2}}\large\frac{\sqrt{1+\cos x}}{(1-\cos x)^{\large\frac{5}{2}}}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\sin^{-1}\sqrt{\large\frac{x}{a+x}}dx\quad(Hint:Put\;x=a\tan^2\theta)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int e^{\tan^{-1}x}\bigg(\frac{1+x+x^2}{1+x^2}\bigg)dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\displaystyle\int\frac{2x-1}{(x-1)(x+2)(x-3)}dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\int\limits_0^{\Large\pi} \large \frac{x}{1+\sin x}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following:$\displaystyle\int\frac{x^2dx}{(x^2+a^2)(x^2+b^2)}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\displaystyle\int\frac{x^2dx}{x^4-x^2-12}$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate the following: $\int\limits_0^{\Large \frac{1}{2}}\frac{dx}{(1+x^2)\sqrt {1-x^2}}$$(Hint:let\;x=\sin\theta)$

asked Jan 14, 2013 by sreemathi.v

1 answer

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