alleryIntegration is the inverse process of:
- limit-taking
- differentiation
- multiplication
- exponentiation
Show answer and solution
Correct answer: B. differentiation
Integration (antidifferentiation) reverses differentiation.
JEE Main Unit 6A: Indefinite Integrals & Fundamental Theorem — practice questions — page 2
Explore 43 free Unit 6A: Indefinite Integrals & Fundamental Theorem questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–43 of 43.
Integration is the inverse process of:Read the answer and worked solution →$\displaystyle\int x^n\,dx$ (for $n\neq -1$) equals:Read the answer and worked solution →$\displaystyle\int \cos x\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \frac{1}{x}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int e^x\,dx$ equals:Read the answer and worked solution →The arbitrary constant $C$ added in an indefinite integral is called the:Read the answer and worked solution →$\displaystyle\int x^2\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \sin x\,dx$ equals:Read the answer and worked solution →The value of $\displaystyle\int_0^1 x\,dx$ is:Read the answer and worked solution →$\displaystyle\int \sec^2 x\,dx$ equals:Read the answer and worked solution →The value of $\displaystyle\int_0^{\pi/2} \cos x\,dx$ is:Read the answer and worked solution →$\displaystyle\int 2x\,dx$ equals:Read the answer and worked solution →The technique used to integrate a product of two functions is called:Read the answer and worked solution →
Worked practice questions
$\displaystyle\int x^n\,dx$ (for $n\neq -1$) equals:
- $x^{n+1} + C$
- $\dfrac{x^{n-1}}{n-1} + C$
- $n x^{n-1} + C$
- $\dfrac{x^{n+1}}{n+1} + C$
Show answer and solution
Correct answer: D. $\dfrac{x^{n+1}}{n+1} + C$
By the power rule for integration, ∫xⁿ dx = x^{n+1}/(n+1) + C for n ≠ −1.
$\displaystyle\int \cos x\,dx$ equals:
- $-\cos x + C$
- $\cos x + C$
- $\sin x + C$
- $-\sin x + C$
Show answer and solution
Correct answer: C. $\sin x + C$
Since d/dx(sin x) = cos x, ∫cos x dx = sin x + C.
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