Integrals Practice Questions

Class 12 · Mathematics · 2245 free MCQs with instant results and detailed explanations.

2245

Total

870

Easy

1004

Medium

371

Hard

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Topics in Integrals

Properties of Definite Integrals 455

Definite Integrals 456

Methods of Integration 725

Indefinite Integrals 609

Sample Questions from Integrals

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) = 3x^2?

A. x^3 + C

B. x^3 + 3C

C. 3x^3 + C

D. x^2 + C

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Correct Answer: A

The integral of 3x^2 with respect to x is (3/3)x^3 = x^3, plus the constant of integration C.

Easy

Which of the following is the integral of sin(x)?

A. -cos(x) + C

B. cos(x) + C

C. sin(x) + C

D. -sin(x) + C

Show Answer & Explanation

Correct Answer: A

The integral of sin(x) with respect to x is -cos(x) + C, based on trigonometric integration rules.

Easy

Find the indefinite integral of the function f(x) = e^x.

A. e^x + C

B. xe^x + C

C. e^x + x + C

D. x + C

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Correct Answer: A

The integral of e^x with respect to x is e^x, since e^x is its own derivative.

Medium

Evaluate the integral ∫(3x^2 - 2x + 1) dx.

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

B. x^3 - x + C

C. x^3 - x^2 + 2x + C

D. 3x^3 - x^2 + 1 + C

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Correct Answer: A

Integrating term by term, we get x^3 - x^2 + x + C.

Medium

Which of the following is the integral of e^(2x)?

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

B. e^(2x) + C

C. 2e^(2x) + C

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

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Correct Answer: A

To integrate e^(ax), divide by 'a'. Here, a = 2.

Medium

Evaluate ∫(x^4 - 4x^2 + 4) dx.

A. (1/5)x^5 - (4/3)x^3 + 4x + C

B. (1/5)x^5 - 2x^3 + 4x + C

C. (1/6)x^6 - 4x + C

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

Show Answer & Explanation

Correct Answer: A

Integrating each term gives (1/5)x^5 - (4/3)x^3 + 4x + C.

Medium

Find the integral ∫(1/x) dx.

A. ln|x| + C

B. e^x + C

C. x + C

D. 1/x + C

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Correct Answer: A

The integral of 1/x is the natural logarithm of the absolute value of x plus a constant.

Hard

Evaluate the integral ∫ (3x^2 + 2x + 1)^(1/2) dx.

A. (2/3)(3x^2 + 2x + 1)^(3/2) + C

B. (1/3)(3x^2 + 2x + 1)^(3/2) + C

C. (1/3)(3x^2 + 2x + 1)^(1/2) + C

D. (2/3)(3x^2 + 2x + 1) + C

Show Answer & Explanation

Correct Answer: A

The integral can be solved using the substitution method, resulting in the expression raised to the power of 3/2.

Hard

Find the indefinite integral ∫ (sin x)^2 dx.

A. (x/2) - (sin(2x)/4) + C

B. -cos x + C

C. (sin x)/2 + C

D. (x/2) + C

Show Answer & Explanation

Correct Answer: A

Using the identity for sin^2, we can transform the integral into a simpler form, which is straightforward to integrate.

Q10

Hard

Evaluate the integral ∫ e^(5x) cos(2e^(5x)) dx.

A. (1/25)e^(5x) sin(2e^(5x)) + C

B. (1/5)e^(5x) sin(2e^(5x)) + C

C. (2/25)e^(5x) sin(2e^(5x)) + C

D. (1/10)e^(5x) sin(2e^(5x)) + C

Show Answer & Explanation

Correct Answer: A

This can be integrated using integration by parts method, recognizing e^(5x) and cos(2e^(5x)).

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Integrals — Class 12 Mathematics Practice Questions Online

This page contains 2245 practice MCQs for the chapter Integrals in Class 12 Mathematics. The questions are organized by difficulty — 870 easy, 1004 medium, 371 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 4 topics, giving you comprehensive coverage of the entire chapter.