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Yukti Vault

JEE Mathematics / Practice

Definite Integration

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Showing 363-367 of 392 questions.

IIT-JEE 1995Question 363
Let $I_m=\displaystyle\int_0^{\pi}\dfrac{1-\cos mx}{1-\cos x}\,dx$. Use mathematical induction to prove that $I_m=m\pi$, $m=0,1,2,\ldots$
Definite Integration

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IIT-JEE 1994Question 364
Show that $\displaystyle\int_{0}^{n\pi+v}|\sin x|\,dx=2n+1-\cos v$ where $n$ is a positive integer and $0\le v<\pi$.
Definite Integration

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IIT-JEE 2003Question 365
If $f$ is an even function then prove that $$\int_0^{\pi/2}f(\cos2x)\cos x\,dx=\sqrt2\int_0^{\pi/4}f(\sin2x)\cos x\,dx.$$
Definite Integration

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JEE Main 2021 (Online) 4th August Evening ShiftQuestion 366
If $u+v+w=91$, and $2u=3v=4w$, then the value of $\displaystyle\int_{u-v+w}^{2u+v+4w}e^{(x-[x])}dx$, where $[x]$ denotes the greatest integer $\le x$, is equal to
Definite Integration
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JEE Main 2021 (Online) 4th August Evening ShiftQuestion 367
The value of the integral $\displaystyle\int_{1}^{6}\dfrac{\log_{e}x\,dx}{\log_{e}x^{2}+\log_{e}\left(x^{2}-14x+49\right)}$ is
Definite Integration
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