JEE Main 2024 (Online) 5th April Morning ShiftQuestion 373
The value of $\displaystyle\int_{-\pi}^{\pi}\dfrac{2y(1+\sin y)}{1+\cos^{2}y}\,dy$ is :
Definite Integration
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Definite Integration
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JEE Main 2024 (Online) 5th April Morning ShiftQuestion 374
The integral $\displaystyle\int_{0}^{\pi/4}\dfrac{136\sin x}{3\sin x+5\cos x}\,dx$ is equal to :
Definite Integration
JEE Main 2024 (Online) 5th April Evening ShiftQuestion 375
If $f(t)=\displaystyle\int_{0}^{\pi}\dfrac{2x\,dx}{1-\cos^{2}t\sin^{2}x}$, $0<t<\pi$, then the value of $\displaystyle\int_{0}^{\pi/2}\dfrac{\pi^{2}\,dt}{f(t)}$ equals $\_\_\_\_\_\_\_\_$ .
Definite Integration
JEE Main 2024 (Online) 5th April Evening ShiftQuestion 376
Let $\beta(m,n)=\displaystyle\int_{0}^{1}x^{m-1}(1-x)^{n-1}dx$, $m,n>0$. If $\displaystyle\int_{0}^{1}\left(1-x^{10}\right)^{20}dx=a\times\beta(b,c)$, then $100(a+b+c)$ equals
Definite Integration
JEE Main 2020 (Online) 6th September Morning ShiftQuestion 377
If $I_1=\displaystyle\int_{0}^{1}\left(1-x^{50}\right)^{100}dx$ and $I_2=\displaystyle\int_{0}^{1}\left(1-x^{50}\right)^{101}dx$ such that $I_2=\alpha I_1$ then $\alpha$ equals to :
Definite Integration