allery$\displaystyle\int_0^\pi \sin x\, dx = ?$
- $0$
- $1$
- $2$
- $\pi$
Show answer and solution
Correct answer: C. $2$
$[-\cos x]_0^\pi = -\cos\pi + \cos 0 = 1 + 1 = 2$.
JEE Advanced Integrals — practice questions
Explore 18 free Integrals questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Integrals with Quill →Integrals questions and exercises with answers
Showing questions 1–18 of 18.
$\displaystyle\int_0^\pi \sin x\, dx = ?$Read the answer and worked solution →If $f$ is **odd** on $[-a, a]$, then $\displaystyle\int_{-a}^{a} f(x)\, dx$ equals:Read the answer and worked solution →$\displaystyle\int_0^1 \dfrac{1}{1 + x^2}\, dx = ?$Read the answer and worked solution →$\displaystyle\int_0^{\pi/2} \sin^2 x\, dx = ?$Read the answer and worked solution →$\displaystyle\int_0^\pi x \sin x\, dx = ?$Read the answer and worked solution →$\displaystyle\int_1^e \ln x\, dx = ?$Read the answer and worked solution →If $\displaystyle I_n = \int_0^{\pi/2} \sin^n x\, dx$, then $I_5 = ?$Read the answer and worked solution →$\displaystyle\int_0^2 [x]\, dx$ where $[x]$ is the greatest integer function:Read the answer and worked solution →Evaluate $\displaystyle\int_0^{10\pi} |\sin x|\, dx$:Read the answer and worked solution →$\dfrac{d}{dx}\left[\displaystyle\int_0^{x^2} \sin(t^2)\, dt\right] = ?$Read the answer and worked solution →$\displaystyle\int_0^{\pi/2} \dfrac{\sin x}{\sin x + \cos x}\, dx = ?$Read the answer and worked solution →$\displaystyle\int_0^{\pi/2} \log(\sin x)\, dx = ?$ (classic)Read the answer and worked solution →$\displaystyle\int_0^{\pi/2} \log(\tan x)\, dx = ?$Read the answer and worked solution →$\displaystyle\int_0^\pi \dfrac{x\sin x}{1 + \cos^2 x}\, dx = ?$Read the answer and worked solution →$\displaystyle\int_0^1 \dfrac{\ln(1+x)}{1+x^2}\, dx = ?$ (Putnam classic)Read the answer and worked solution →Match the integral to its resultRead the answer and worked solution →Order the steps to integrate ∫ x·eˣ dx by partsRead the answer and worked solution →Evaluate the definite integralRead the answer and worked solution →
Worked practice questions
If $f$ is **odd** on $[-a, a]$, then $\displaystyle\int_{-a}^{a} f(x)\, dx$ equals:
- $0$
- $2\int_0^a f(x)dx$
- $a$
- Cannot be determined
Show answer and solution
Correct answer: A. $0$
By symmetry, odd-function integrals over symmetric intervals vanish.
(For even $f$: $2\int_0^a f$.)
$\displaystyle\int_0^1 \dfrac{1}{1 + x^2}\, dx = ?$
- $\pi/2$
- $\pi/4$
- $\pi$
- $1$
Show answer and solution
Correct answer: B. $\pi/4$
$[\arctan x]_0^1 = \arctan 1 - \arctan 0 = \pi/4$.
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