# Recently Active Calculus Questions

• Find âˆ« ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...
replied2012-05-08 05:21:35
• \hspace{-16}\bf{\int_{0}^{\frac{\pi}{4}}\ln \left(\frac{1+\sin^2 2x}{\sin^4 x+\cos^4 x}\right)dx} ...
replied2012-05-02 21:56:03
• \hspace{-16}\bf{\int_{-1}^{1}\frac{2x^{1004}+x^{3014}+x^{2008}.\sin(x)^{2007}}{1+x^{2010}}dx} ...
replied2012-05-02 21:35:01
• \hspace{-16}\bf{\int_{0}^{4\pi}\ln\left|13.\sin (x)+3\sqrt{3}.\cos (x)\right|dx}= ...
replied2012-05-02 10:48:40
• \hspace{-16}\bf{\int\frac{x^2.\cos^{-1}\big(x\sqrt{x}\big)}{\big(1-x^3\big)^2}dx} ...
replied2012-04-28 00:33:25
• \hspace{-16}\bf{\int_{\frac{25\pi}{4}}^{\frac{53\pi}{4}}\frac{1}{(1+2^{\sin x}).(1+2^{\cos x})}dx} ...
• \hspace{-16}\bf{\lim_{n\rightarrow \infty}\sum_{i=0}^{n}\;\sum_{j=0}^{n-i}\frac{x^j}{i!\;.\;j!}=} ...
• ...
replied2012-04-27 01:08:17
• \hspace{-16}\bf{(1)\;\; \int_{0}^{\infty}\frac{\ln (x)}{x^2+4}dx}$\\\\\\$\bf{(2)}\;\;$Find Max. value of$\bf{\int_{0}^{1}f^3(x)dx}$\\\\\\ Given$\bf{\mid f(x)\mid \leq 1}$and$\bf{\int_{0}^{1}f(x)dx=0}$\\\\\\$\bf{(3)\;\; ...
replied2012-04-26 22:32:31
• \int_{\pi /2}^{5\pi /2}{ \frac{e^{tan^{-1}(sinx)}}{e^{tan^{-1}(sinx) }+ e^{tan^{-1}(cosx)}}} dx A)1 B)Ï€ C)e D)none of these ...
replied2012-04-26 22:31:21
• \hspace{-16}$Let$\bf{a\in \mathbb{R}}$. If the value of$\bf{\int_{-\pi+a}^{3\pi+a}\mid x-a-\pi\mid\sin \left(\frac{x}{2}\right)dx=-16}$\\\\\\ Then Sum of all Integer value of$\bf{a}$in$\bf{\left[0,314\right]}$is$\bf{k\ ...
replied2012-04-26 08:00:26
• \hspace{-16}\bf{\int \frac{\sin^2(2012\; x)}{\sin \; (x)}dx} ...
• consider a function f on non-negative integers such that f(0)=1 , f(1)=0 and f(n) + f(n-1) = nf(n-1) + (n-1)f(n-2) for nâ‰¥2 . Show that , \frac{f(n)}{n!} = \sum_{k=0}^{n}{\frac{(-1)^{k}}{k!}} ...
replied2012-04-26 00:33:50
• \hspace{-16}\mathbf{\lim_{n\rightarrow \infty}\sum_{r=0}^{n}\frac{1}{\binom{n}{r}}=} ...
replied2012-04-24 22:01:49
• \hspace{-16}\bf{\int_{-\pi}^{\pi}\frac{\sin (0.5+n)x}{2\sin (0.5)x}dx=}$\\\\\\ Where$\mathbf{n\in\mathbb{N}}$and$\bf{0.5=\frac{1}{2}}$... replied2012-04-24 18:55:28 • find âˆ« x3-2/ (x3+1)3 dx ... replied2012-04-24 12:06:45 • \hspace{-16}\mathbf{\int_{1}^{\infty}\frac{(x^3+3)}{x^6.(x^2+1)}dx=\frac{a+b\pi}{c}}$.\\\\\\ Then $\mathbf{(a,b,c)=}$ ...
replied2012-04-24 07:27:02
• âˆ« x2+x-1/x3+x2 -6x dx ...
replied2012-04-24 07:13:52
• Please suggest a good book for solving quality calculus problems for JEE preparation. ...
replied2012-04-21 22:13:51
• \hspace{-16}$Let$\bf{L=\lim_{n\rightarrow \infty}\frac{1}{\frac{1}{\sqrt{2}}.\sqrt{\big(\frac{1}{2}}+\frac{1}{2}\sqrt{\frac{1}{2}}\big).\sqrt{\big(\frac{1}{2}}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}...... ...
• âˆ«l log x/x1/2 upper limit 1 lower limit 0 form the positive side ...
replied2012-04-19 03:39:23
• lim (1+3x)10/x as xâ†’0+ ...
replied2012-04-19 03:17:48
• \hspace{-16}\bf{\int \big(x-\sqrt{x^2+1}\big)^{2012}dx} ...
replied2012-04-18 04:18:07
• \hspace{-16}$If$\bf{x,y,z\in \mathbb{R}}$and$\bf{f(x).f(y).f(z) = 12f(xyz) ô€€€ -16xyz}$\\\\ Then No. of function which satisy$\bf{f:\mathbb{R}\rightarrow \mathbb{R}}$is ... replied2012-04-18 02:50:38 • âˆ«sin2(log x) dx also âˆ« log x/(1 + log x)2 dx ... replied2012-04-16 08:37:24 • âˆ«[ ( x2 + 1 ) / ( x4 + 1) ] dx ... replied2012-04-10 01:46:58 • \hspace{-16}$If $\bf{f(1)=1}$ and $\bf{f(x+5) > f(x) +5 f(x+1) < f(x) + 1}$\\\\ and $\bf{g(x)=f(x)-x+1}$.Then $\bf{g(2012)}$ is ...
replied2012-04-08 10:33:30
• if x*tan(y) + 1 = (1+x^2)^(1/2) , find dy/dx. ...
replied2012-04-06 01:49:32
• \int_{0}^{x}{f(t)d(t)} ----> 5 as |x| ---> 1, then value of 'a' so that the equation 2x + \int_{0}^{x}{f(t)d(t)} = a has at least two roots of opposite signs in (-1,1) is a) 0<a<1 b) 0<a<3 c) -1<a<âˆž ...
replied2012-04-05 07:24:00
• let f be a one to one continuous function such that f(2) =3and f(5)=7. given (2to5)âˆ« f(x) dx =17 then value of (3to7)âˆ« f-1(x) dx is (a) 10 (b) 11 (c)12 (d) 13 ans c 2 if nCk is cmbination of n diff. thing taking k at a ti ...
replied2012-04-05 06:08:01