Integral Calculus Practice Questions

JEE · Mathematics · 1623 free MCQs with instant results and detailed explanations.

1623

Total

403

Easy

751

Medium

469

Hard

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Topics in Integral Calculus

Indefinite Integrals 584

Area Under Curves 569

Definite Integrals 470

Sample Questions from Integral Calculus

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

What is the indefinite integral of the function f(x) = 2x + 3?

A. x^2 + 3x + C

B. x^2 + 3x

C. 2x^2 + 3x + C

D. 2x^2 + 3x

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Correct Answer: A

The indefinite integral of a polynomial function is found by increasing the power of each term by one and dividing by the new power, while adding a constant of integration (C). Here, integrating 2x gives x^2, and integrating 3 gives 3x, hence the result is x^2 + 3x + C.

Easy

What is ∫ (3x^2 + 2x + 1) dx?

A. x^3 + x^2 + x + C

B. x^3 + x^2 + C

C. x^3 + C

D. 3x^3 + 2x^2 + C

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Correct Answer: A

Integrating term-by-term gives x^3 + x^2 + x + C.

Easy

What is the integral of e^x?

A. e^x + C

B. xe^x + C

C. x + C

D. e^x/x + C

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Correct Answer: A

The integral of e^x is e^x plus a constant of integration.

Medium

What is the integral of sin(2x) with respect to x?

A. -cos(2x)/2 + C

B. cos(2x)/2 + C

C. -sin(2x)/2 + C

D. sin(2x)/2 + C

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Correct Answer: A

The integral of sin(kx) is -cos(kx)/k. Here, k=2, thus -cos(2x)/2 + C.

Medium

Evaluate the integral ∫ (3x^2 + 4) dx.

A. x^3 + 4x + C

B. x^3 + 4x^2 + C

C. x^3 + 4/x + C

D. 3x^3 + 4x + C

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Correct Answer: A

The integral of x^n dx is (x^(n+1))/(n+1) + C. Here, integrate each term separately.

Medium

Find ∫ (1/(x^2 + 4)) dx.

A. (1/2)tan^(-1)(x/2) + C

B. (1/4)tan^(-1)(x/2) + C

C. (1/2)ln|x^2 + 4| + C

D. tan^(-1)(x/2) + C

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Correct Answer: A

The integral of 1/(a^2 + x^2) is (1/a)tan^(-1)(x/a) + C. Here, a=2.

Medium

What is the integral of e^(3x) with respect to x?

A. (1/3)e^(3x) + C

B. 3e^(3x) + C

C. e^(3x) + C

D. 3/e^(3x) + C

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Correct Answer: A

The integral of e^(kx) is (1/k)e^(kx) + C. Here, k=3.

Hard

Evaluate the integral ∫ (x^2 + 2x + 1)/(x + 1)^2 dx.

A. x + C

B. x + ln|x + 1| + C

C. x + 1 + C

D. x - ln|x + 1| + C

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Correct Answer: B

The integral can be simplified and solved using partial fractions, leading to the logarithmic term.

Hard

Determine the integral ∫ (x^3 - 3x^2 + 2x) e^x dx.

A. (x^3 - 3x^2 + 2x)e^x + C

B. (x^3 - 3x^2 + 2)e^x + C

C. (x^3 - 3x^2 + 1)e^x + C

D. (x^3 - 3x^2 + 3)e^x + C

Show Answer & Explanation

Correct Answer: A

Integration by parts is the key method here, applied multiple times to reduce the polynomial degree.

Q10

Hard

Calculate ∫ x e^(x^2) dx.

A. (1/2)e^(x^2) + C

B. (1/2)x^2 e^(x^2) + C

C. e^(x^2) + C

D. (1/4)e^(x^2) + C

Show Answer & Explanation

Correct Answer: A

Using the substitution method, where u = x^2 simplifies the integral effectively.

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Integral Calculus — JEE Mathematics Practice Questions Online

This page contains 1623 practice MCQs for the chapter Integral Calculus in JEE Mathematics. The questions are organized by difficulty — 403 easy, 751 medium, 469 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.