Application of Integrals Practice Questions

Class 12 · Mathematics · 1878 free MCQs with instant results and detailed explanations.

1878

Total

584

Easy

935

Medium

359

Hard

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Topics in Application of Integrals

Area between Curves 925

Area under Curves 953

Sample Questions from Application of Integrals

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

Easy

What is the area between the curve y = x^2 and the x-axis from x = 0 to x = 2?

A. 2/3

B. 4/3

C. 2

D. 4

Show Answer & Explanation

Correct Answer: B

The area is calculated by integrating x^2 from 0 to 2, which gives (2^3)/3 = 8/3.

Easy

Find the area enclosed by the curve y = 3x and the line y = 12.

A. 15

B. 18

C. 24

D. 30

Show Answer & Explanation

Correct Answer: C

To find the area, we need to determine the intersection points and integrate.

Easy

Calculate the area under the curve y = sin(x) from x = 0 to x = π/2.

A. 1

B. 2

C. π/2

D. π

Show Answer & Explanation

Correct Answer: A

The integral of sin(x) from 0 to π/2 is -cos(x) evaluated from 0 to π/2, which gives 1.

Medium

What is the area under the curve y = x^2 from x = 0 to x = 2?

A. 2

B. 4/3

C. 8/3

D. 4

Show Answer & Explanation

Correct Answer: C

The area under y = x^2 from 0 to 2 is calculated using the integral ∫(x^2)dx from 0 to 2, which equals 8/3.

Medium

Determine the area under the curve y = sin(x) from x = 0 to x = π.

A. 1

B. 2

C. 0

D. π

Show Answer & Explanation

Correct Answer: B

The area is calculated by integrating sin(x) from 0 to π, resulting in 2.

Medium

What is the area enclosed between y = x^2 and y = 4?

A. 8/3

B. 16/3

C. 4

D. 2

Show Answer & Explanation

Correct Answer: B

The area is calculated using ∫(4 - x^2)dx from -2 to 2, resulting in 16/3.

Medium

Calculate the area under the curve y = e^x from x = 0 to x = 1.

A. e-1

B. e-1/e

C. e

D. 1

Show Answer & Explanation

Correct Answer: A

The area is found by integrating e^x from 0 to 1, which results in e - 1.

Hard

Calculate the area between the curve y = x^2 and the line y = 4.

A. 8

B. 16/3

C. 12

D. 8/3

Show Answer & Explanation

Correct Answer: B

The area can be calculated by integrating the difference between the line and the curve over the interval determined by their points of intersection.

Hard

Find the area under the curve y = sqrt(x) from x = 1 to x = 9.

A. 12

B. 18

C. 24

D. 36

Show Answer & Explanation

Correct Answer: B

The area under the curve can be found by integrating the function from 1 to 9, which gives the required area.

Q10

Hard

Determine the area enclosed between the curves y = x^3 and y = x.

A. 1

B. 2

C. 3/2

D. 4/3

Show Answer & Explanation

Correct Answer: C

The area can be found by identifying the points of intersection and integrating the difference of the two curves.

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Application of Integrals — Class 12 Mathematics Practice Questions Online

This page contains 1878 practice MCQs for the chapter Application of Integrals in Class 12 Mathematics. The questions are organized by difficulty — 584 easy, 935 medium, 359 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 2 topics, giving you comprehensive coverage of the entire chapter.