Recent questions in Integrals

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^1x\;(1-x)^n\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

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}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^2x\sqrt{2-x}dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals, evaluate the integral $\int\limits_0^\frac{\Large \pi}{\Large 2}(2 \log \sin x-\log \sin 2x)\;dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^2\;x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\pi\frac{x\;dx}{1+\sin x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^7\;x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^{2\pi}\cos^5x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^\frac{\Large \pi}{\Large 2}\frac{\sin x-\cos x}{1+\sin x\cos x}\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^a\frac{\sqrt x}{\sqrt x+\sqrt{a-x}}dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Show that $\int\limits_0^af(x)g(x)dx=2\int\limits_0^af(x)dx,$ if $f$ and $g$ are defined as $f(x) = f(a - x)$ and $g(x) + g(a - x)=4$

asked Dec 3, 2012 by sreemathi.v

1 answer

Choose the correct answer in the value of $\displaystyle\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}(x^3+x\cos x+\tan^5x+1)dx$ is

asked Dec 3, 2012 by sreemathi.v

1 answer

Choose the correct answer in the value of $\int\limits_0^\frac{\pi}{2}log\bigg(\frac{\large 4+3\sin x}{\large 4+3\cos x}\bigg)dx$ is

asked Dec 3, 2012 by sreemathi.v

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

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