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Class12

Relations and Functions

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Application of Derivatives

Integral Calculus

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Integrate : $\int \large \frac{e^{\Large a \sin ^{-1} x}}{\sqrt {1-x^2}}$ $.dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \sqrt x e^{\large (x)^{3/2}} \cos (e^{\large(x)^{3/2}}. dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \sin 4x \cos 4x\;dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\large\frac{(1+ \log x)^4}{x}$ $dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{\tan^2 (\sqrt x)}{\sqrt x}$ $.dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate: $\int \sqrt {x^2+4x+4}.dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate: $\int \large\frac{e^{-\tan ^{-1}(a^x)}}{[1+(a^x)^2]}$ $a^x.dx$

asked Dec 19, 2013 by meena.p

1 answer

integrate : $\int \sec^3 x dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \sin ^3 x .dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \sqrt {4x-x^2}dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{8}{9} \frac{x}{\sqrt {1-x^4}}$ $dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \large\frac {e^{2x}+e^{-2x}}{e^{2x}-e^{-2x}}$ $dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int e^x (a e^x+b)^n. dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \sqrt{\sin ^3 x}. \cos x \;dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int x \sec ^2x^2 .dx$

asked Dec 19, 2013 by meena.p

1 answer

Integrate: $\int \large\frac{\Large e^{\tan ^{-1}(m)}}{1+m^2}$ $.dm$

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{(1-2x^2)^2}{x^{3/2}}$ $dx$

asked Dec 19, 2013 by meena.p

1 answer

$f'(x) = a \cos x + b \sin x ;\; f'(0)=4;\; f(0)=3;\; f \bigg(\large\frac{\pi}{2}\bigg)$ $=5$ . Find the value of $\;f(x)\;$ ?

asked Dec 19, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{\cos 2x}{\cos ^2 x \sin ^2 x }$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{x^5+1}{x^2+1}$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int\large\frac{\cos 2x}{\cos ^ 2 x}$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{2^x+3^x}{6^x}$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \sin ^2 x \cos ^2 x \;dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \sin ^2 x. \cos ^2 x \;dx$

asked Dec 18, 2013 by meena.p

1 answer

integrate : $\int \large\frac{1}{\sin ^2 x \cos ^2 x }$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int (1+2x) (3+4x) .dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{ e^{5x}+e^{-7x}}{e^{2x}}$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\sqrt { \bigg( \large\frac{1+ \sin 2x}{1+ \cos 2x}\bigg)}$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \bigg( x^2 +\large\frac{1}{x^2}\bigg)^3$ $dx$

asked Dec 18, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{\sin x}{1-\sin x}$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

Integrate: $\int \large\frac{(x^3+5x^2-3)}{(x+1)}$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1}{(x)^{5/2}}$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1}{1+\cos x }$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{a \sin x +b}{\cos^2 x }$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

Integrate : $\int \large\frac{1}{1+\cos x}$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

$I_n =\int \limits_0^{z/4} \tan ^n x \;dx$ find $I_{n-1}+I_{n+1}$

asked Dec 17, 2013 by meena.p

1 answer

$\int \limits_0^a x dx < a+4$ then

asked Dec 17, 2013 by meena.p

1 answer

Integrate : $\int \limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \large\frac{\log (5 - \theta \sin \theta)}{\log (5+\theta \sin \theta)}$ $d \theta$

asked Dec 17, 2013 by meena.p

1 answer

If $\overrightarrow a,\:\overrightarrow b$ are two non zero and non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$

asked Dec 17, 2013 by rvidyagovindarajan_1

1 answer

Integrate : $\int \limits _0^{\frac{\pi}{4}} \large\frac{\sec x cosec x}{\log (\tan x)}$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

$\int \limits _0^{\omega} \large\frac{x^2}{(x^2+a^2) (x^2+b^2) (x^2+c^2)}$ $dx= \large\frac{\pi}{2(a+b)(b+c)(c+a)}$ then find $\int \limits _0^{\omega} \large\frac{dx}{(x^2+4)(x^2+g)}$

asked Dec 17, 2013 by meena.p

1 answer

$\int \limits_1^6 (6-4x) dx \leq 6-5b \;\&\;6 > 1$ Find 'b' value

asked Dec 17, 2013 by meena.p

1 answer

Integrate : $\int \limits_0^{\frac{\pi}{2}} \large\frac{\phi(x)}{\phi (\Large\frac{\pi}{2}-x)+\phi (x)}$ $dx$

asked Dec 17, 2013 by meena.p

1 answer

$\int \limits_{-\pi}^{\pi} (\cos px - \sin q x)^2 dx$ where $p \;\&\; q$ are whole number. Find its value.

asked Dec 17, 2013 by meena.p

1 answer

Integrate: $\int \limits_0^{\rho} \large\frac{y.dy}{\sqrt {y+\rho}}$

asked Dec 17, 2013 by meena.p

1 answer

Integrate: $\int \limits_0^{\rho} \large\frac{y.dy}{\sqrt {y+\rho}}$

asked Dec 17, 2013 by meena.p

0 answers

Integrate: $\int\limits _0^{\pi} e^x \sin x dx$

asked Dec 17, 2013 by meena.p

1 answer

If $g(x) =\large\frac{f(x) +f(-x)}{2}$ defined over $[-3,3]$ and $f(x)=2x^2-4x+1$ then $\int \limits_{-3}^3=?$

asked Dec 17, 2013 by meena.p

1 answer

Integrate: $\int \limits_0^{\large\frac{\pi}{2}} \sin x \sin 2x \;dx$

asked Dec 16, 2013 by meena.p

1 answer

Integrate: $\int \limits_{0}^{\large\frac{\pi}{2}} \large\frac{\cos x}{(1+\sin x)(2+ \sin x)}$ $dx$

asked Dec 16, 2013 by meena.p

1 answer

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