Mathematics · 2016
JEE Main · 10 April 2016, Shift 1 · Q74
The integral ∫ (d x)/((1+√ x ) √(x-x^2)) is equal to: (where C is a constant of integration.)
The integral $\displaystyle \int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}$ is equal to :
(where C is a constant of integration.)
Official answer
(2)
$\displaystyle -2 \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+\mathrm{C}$
More from Indefinite Integration
- The integral ∫ √(1+2 cot x(cosec x+ cot x)) d x (0<x<(π)/2) is equal to: (where C is a constant of integration)2017
- If ∫ 1/x √((1-x)/(1+x)) d x=g(x)+c, g(1)=0, then g(1/2) is equal to:2022
- The integral ∫ x cos^-1((1-x^2)/(1+x^2)) d x(x>0) is equal to:2014
- If ∫ (cos x d x)/(sin^3 x(1+ sin^6 x)^2 / 3)=f(x)(1+ sin^6 x)^1 / λ+c where c is a constant of integration, then λ f((π)/3) is equal to:2020
- The integral ∫ (sin^2 x cos^2 x)/(( sin^3 x+ cos^3 x)^2) d x is equal to:2014
- The integral ∫ (d x)/(x^2(x^4+1)^3 / 4) equals:2015
- Let f(x)=∫ (d x)/((3+4 x^2) √(4-3 x^2)),|x|<2/(√3). If f(0)=0 and f(1)=1/(α β) tan^-1((α)/(β)), α, β>0, then α^2+β^2 is equal to ____.2023
- If ∫ (log (t+√(1+t^2)))/(√(1+t^2)) dt=1/2( g(t))^2+C, where C is a constant, then g(2) is equal to:2015
JEE Main 2016 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.