Recently Active Calculus Questions

if y = x/ln|cx| where c is a arbitrary constant, is the general son. of differential equation dy/dx = y/x + \phi \left(\frac{x}{y} \right) , then the function \phi \left(\frac{x}{y} \right) is--- ans.----> - y2/x2 ...

\int \frac{sinx+sin^{3}x}{cos2x}dx = Acosx + Blog\left|f(x) \right| + c A) A=1/4,B=-\frac{1}{\sqrt{2}}, f(x)=\frac{\sqrt{2}cosx -1}{\sqrt{2}cosx +1} B) A=1/2,B=-\frac{3}{4\sqrt{2}}, f(x)=\frac{\sqrt{2}cosx +1}{\sqrt{2}cosx -1 ...

\int \frac{1}{2e^{2x}+3e^{x}+1}dx ans ------> -\frac{1}{2}log\left| e^{-2x}+3e^{-x}+2 \right| + \frac{3}{2}log \left|\frac{e^{-x}+1}{e^{-x}+2} \right| + c ...

\int \frac{t. ( 1- t ^2 ) ^{\frac{-7}{4}}}{ \sqrt{t + 4 }.\sqrt{1- t^2 }+ \sqrt{t+ 5 }.\sqrt{1- t^2}} ...

\int \left(\frac{cotx+cosecx-1}{cotx - cosecx+1} \right)dx ans ------> ln\left|2sin^{2}\frac{x}{2} \right|+c ...

Q1. \int_{-1}^{1}{\frac{d(tan^{-1}\frac{1}{x})}{dx}dx} Q2. \int_{-1}^{3}{(tan^{-1}\frac{x^2+1}{x}+tan^{-1}\frac{x}{x^2+1})dx} ...

\int (x^{2}+2x + 3)\sqrt{x^{2}+x+1}dx please help. ans nahin pata mujhe... full soln. hi likhiyo. aur haan dekhene walon sirf dekho maat try karo aur post the soln. ...

2e^{-1/4}<\int_{0}^{2}{e^{x^{2}-x}}dx<2e^{2} .PROVE THE INEQUALITY. this one is definitely a mind freak. ...

\int_{0}^{1} \left(1- x^2 \right)^{\frac{5}{2}} ...

\int \left\{1+ 2tanx(tanx + secx ) \right\}^{1/2}dx ans---> lnsecx(secx + tanx) +c ...

\int \frac{cosx - sinx}{\sqrt{8-sin2x}}dx ans-----> sin ^{-1}\left(\frac{sinx + cosx}{3} \right)+c ...

\int f(x)sinxcosx dx = \frac{1}{2(a^{2}-b^{2})}log (f(x)) + c THEN f(x) = ???? ans GIVEN ----> \frac{1}{a^{2}sin^{2}x + b^{2}cos^{2}x} ...

find the minimum value of (3sinx-4cosx-10) * (3sinx+4cosx-10) ...

∫ dx/xn(1+xn) 3/n solve it someone... that is (1+xn) to the power 3/n ...

*Image* how u solve it ? ...

Determine as many solutions as you can to each of the following functional equations: 1.f(x) f(x + 1) = f(2 x + 1) 2. f(x) f(x + 1) = f[f(x) + x] ...

*Image* *Image* ...

If ∫ [ 0 to pi/2 ] dx / [a2 cos2 x + b2 sin2x ] = pi/2ab Then the value of ∫[0 to pi/2] dx / [ 4 cos2x + 9 sin2x ]2 = ??? (A) 11 pi / 864 (B) 13 pi/864 (C) 17 pi/864 (D) None ...

\int \frac{\sqrt{x^2 + 1}\left\{log( x^2 + 1 ) - 2log x \right\}.dx}{x^ 4} ...

question is as mentioned by SR (SEE DOWN) ANS ----> cot A { log sec(x+A) - log sec x} ...

*Image* ANS - > MUJHE NAHIN MALUM ...

IF ∫(sin 3θ + sin θ)esin θ cos θ dθ = (Asin 3θ + Bcos 2θ + Csin θ + D cos θ + E)esin θ + c find A, B , C , D , E ANS---> -4 , -12 , -20 , 0 , 32 respectively ...

IF ∫(sin 3θ + sin θ)esin θ cos θ dθ = (Asin 3θ + Bcos 2θ + Csin θ + D cos θ + E)esin θ + c find A, B , C , D , E ANS---> -4 , -12 , -20 , 0 , 32 respectively ...

\int \frac{\sqrt{x}dx }{1- x} another for practice 2. \int_{0}^{\frac{\pi }{2}}{ \frac{sinx cosx dx }{ cos^2x + 3cosx + 2}} ...

\int \frac{ dx}{ (a^2 sin^2x + b^2 cos^2x ) ^2} ...

Statement 1: f(x) = \left | x \right |cosx is NOT differentiable at x=0 Statement 2: Every Absolute value functions are NOT differentiable. EXPLAIN YOUR ANSWER. ...

Lim\; n\to \infty \; \frac{1}{n^{2}} \; \sum_{k=0}^{n-1}\: \: \begin{bmatrix} k\int_{k}^{k+1}((x-k)(k+1-x))^{1/2} \end{bmatrix} A) π/32 B) π/16 C) π/8 D) π/4 ...

Find: \lim_{x\to\infty} \left(\dfrac{ex}{2}+x^2\left\{\left(1+\dfrac{1}{x}\right)^x-e\right\}\right) Note that {.} is NOT the fractional part. ...

Positive value of a so that the definite integral \int_{a}^{a^{2}} \frac{dx}{x+x^{\frac{1}{2}}} achieves the smallest value is: A) tan2(Ï€/8) B) tan2(3Ï€/8) C) tan2(Ï€/12) D) 0 ...

True/ False: If f is differentiable then f\left | f \right | is also differentiable. Give Reason. ...