Recent questions tagged misc

Choose the correct answer in the the area bounded by the curve $y = x |\; x\; | ,\; x$ - axis and the ordinates $x = -1$ and $x = 1$ is given by [Hint : $y = x^2$ if $x > 0$ and $y = -x^2$ if $x < 0$].

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the the area of the circle $x^2 + y^2 = 16$ exterior to the parabola $y^2 = 6x$ is \[\begin{array} (A) \frac{4}{3} (4\pi - \sqrt 3) \quad &(B) \frac{4}{3} (4\pi + \sqrt 3) \quad & (C) \frac{4}{3} (8\pi - \sqrt 3) \quad & (D) \frac{4}{3} (8\pi + \sqrt 3) \end{array}\]

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the the area bounded by the $y$ - axis, $y = \cos\: x$ and $y = \sin\: x$ when $0 \leq x \leq \frac{\large \pi}{2}$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function\[\frac{5x}{(x+1)(x^2+9)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\large\int\frac{\sin x}{\sin(x-a)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\frac{e^{5logx}-e^{4logx}}{e^{3logx}-e^{2logx}}\end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\int\frac{\cos x}{\sqrt{4-\sin^2x}} \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{\sin^8x-\cos^8x}{1-2\sin^2x\cos^2x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{\cos(x+a)\cos(x+b)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\int\frac{x^3}{\sqrt{1-x^8}} \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{e^x}{(1+e^x)(2+e^x)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{(x^2+1)(x^2+4)}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\cos^3x\;e^{log\sin x}dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int e^{3\log x}(x^4+1)^{-1}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int f'(ax+b)[f(ax+b)]^n\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\large\frac{1}{\sqrt{\sin^3x\sin(x+\alpha)}}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{\sin^{-1}\sqrt x-\cos^{-1}\sqrt x}{\sin^{-1}\sqrt x+\cos^{-1}\sqrt x},$$x\;\in\;[0,1]$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\sqrt{\frac{1-\sqrt x}{1+\sqrt x}}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{2+\sin2x}{1+\cos2x}$$e^x$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{x^2+x+1}{(x+1)^2(x+2)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\tan^{-1}\sqrt{\frac{1-x}{1+x}}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{\sqrt{x^2+1}[log(x^2+1)-2logx]}{x^4}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_\frac{\pi}{2}^\pi e^x\bigg(\frac{1-\sin x}{1-\cos x}\bigg)dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{4}\frac{\sin x\cos x}{\cos^4x+\sin^4x}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{2}\frac{\cos^2xdx}{\cos^2x+4\sin^2x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_\frac{\pi}{6}^\frac{\pi}{3}\frac{\sin x+\cos x}{\sqrt{\sin2x}}dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^1\frac{dx}{\sqrt{1+x}-\sqrt x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{4}\frac{\sin x+\cos x}{9+16\sin 2x}\;dx\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals\[\int\limits_0^\frac{\pi}{2}\sin 2x\tan^{-1}(sin x)\;dx\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals $\int\limits_0^{\pi}\large\frac{x\tan x}{\sec x+\tan x}$$\;dx$

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate the definite integrals: $\int\limits_1^4 [\; |x-1|+|x-2|+|x-3|\;]dx$

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_1^3\frac{dx}{x^2(x+1)}=\frac{2}{3}+log\frac{2}{3}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^1x\;e^x\;dx=1\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_{-1}^1x^{17}\cos^4x\;dx=0\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^\frac{\pi}{2}\sin^3x\;dx=\frac{2}{3}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^\frac{\pi}{4}2\tan^3x\;dx=1-log2\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Prove the following\[\int\limits_0^1\sin^{-1}x\;dx=\frac{\pi}{2}-1\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Evaluate $ \large \int\limits_0^1e^{2-3x}\;$$dx\;$ as a limit of a sum

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers in $\int\frac{dx}{e^x+e^{-x}}$ is equal to

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers in $\int\frac{\large \cos 2x}{\large (\sin x+\cos x)^2}dx$ is equal to

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers if $f(a+b-x) = f(x)$ , then $\int\limits_a^bx\;f(x)dx$ is equal to

asked Dec 2, 2012 by sreemathi.v

1 answer

Choose the correct answers in the value of $\int\limits_0^1\tan^{-1}\bigg(\frac{\large 2x-1}{\large 1+x-x^2}\bigg)dx\;is$\[(A)\;1\qquad(B)\;0\qquad(C)\;-1\qquad(D)\;\frac{\pi}{4}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}\qquad[Hint:\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}=\frac{1}{x^\frac{1}{3}\bigg(1+x^\frac{1}{6}\bigg)},put\;x=t^6]\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{x^2(x^4+1)^\frac{3}{4}}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{x\sqrt{ax-x^2}}[Hint:Put\;x=\frac{a}{t}]\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\frac{1}{\sqrt{x+a}+\sqrt{x+b}}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{1}{x-x^3}\]

asked Dec 2, 2012 by sreemathi.v

1 answer

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\hat{r}. (\hat{i}+\hat{j}+\hat{k}) = 2$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that if a plane has the intercepts $a, b, c$ and is at a distance of $p$ units from the origin, then $\large\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} = \frac{1}{p^2}$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Prove that \[sin^{-1} \frac{8}{17} +sin^{-1} \frac{3}{5} =tan^{-1} \frac{77}{36}\]

asked Nov 29, 2012 by vaishali.a

1 answer

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