💬 Discord
Login

Area Under Curves Practice Questions

JEE · Mathematics · 1656 free MCQs with instant results and detailed explanations.

1656
Total
333
Easy
722
Medium
601
Hard

Start Practicing Area Under Curves

Take a timed quiz or customize your practice session

Quick Quiz (10 Qs) → Mock Test (25 Qs) ⚙ Customize

Topics in Area Under Curves

Area Between Curves 552
Standard Curves 566
Area Using Integration 538

Sample Questions from Area Under Curves

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

Q1
Easy
What is the area between the curves y = ln(x) and y = 1 from x = 1 to e?
A. 1
B. 2
C. 0.5
D. 3
Show Answer & Explanation
Correct Answer: A
The area can be computed as the integral of (1 - ln(x)) from 1 to e.
Q2
Easy
What is the area between y = 4 - x^2 and y = 0 from x = -2 to x = 2?
A. 4π/3
B. 8
C. 4
D. 6
Show Answer & Explanation
Correct Answer: C
The area can be derived from integrating (4 - x^2) across the interval from -2 to 2.
Q3
Easy
Determine the area between y = e^x and y = e^(-x) from x = 0 to x = 1.
A. 1
B. e - 1/e
C. 2
D. e + 1/e
Show Answer & Explanation
Correct Answer: B
The area can be calculated by integrating the difference of the two exponential functions.
Q4
Medium
Calculate the area enclosed between the curves y = sin(x) and y = cos(x) for 0 ≤ x ≤ π/4.
A. 1/√2
B. 1/4
C. 1/2
D. 1/√2 - 1/4
Show Answer & Explanation
Correct Answer: D
The area is found by integrating the difference of the two curves over the interval. The curves intersect at x = π/4, and the integral of (cos(x) - sin(x)) from 0 to π/4 gives the area.
Q5
Medium
Determine the area between y = ln(x) and y = 1 from x = 1 to x = e.
A. 1
B. 2
C. e - 1
D. 0
Show Answer & Explanation
Correct Answer: A
Integrating (1 - ln(x)) from 1 to e gives the area. Using the properties of logarithms, the result is 1.
Q6
Medium
What is the area bounded by the curves y = cos(x) and y = 0 for the interval [0, π/2]?
A. 1
B. 0.5
C. π/2
D. 2
Show Answer & Explanation
Correct Answer: A
The area is given by the integral of cos(x) from 0 to π/2, which equals 1.
Q7
Medium
What is the area between y = e^x and y = 0 from x = 0 to x = 1?
A. e - 1
B. 1
C. 2
D. e
Show Answer & Explanation
Correct Answer: A
The area is calculated by integrating e^x from 0 to 1, which results in e - 1.
Q8
Hard
Determine the area between the curves y = sin(x) and y = cos(x) from x = 0 to x = π/4.
A. 1/√2
B. 1
C. √2 - 1
D. 0
Show Answer & Explanation
Correct Answer: C
To find the area, calculate the integral of the upper curve minus the lower curve from the intersection points.
Q9
Hard
Determine the area between the curves y = sin(x) and y = cos(x) over the interval [0, π/4].
A. 1/2 - sqrt(2)/4
B. 1/2 + sqrt(2)/4
C. 0
D. 1/4
Show Answer & Explanation
Correct Answer: A
The area is obtained by integrating the absolute difference of the functions over the interval.
Q10
Hard
Find the area between the curves y = ln(x) and y = 2 - x^2 for x = 1 to x = 2.
A. 3/2 - 1/e
B. 1/e
C. 1/2
D. 2 - 1/e
Show Answer & Explanation
Correct Answer: A
The area is given by ∫[1 to 2] ((2 - x^2) - ln(x)) dx after determining that the upper curve is (2 - x^2) in this interval.

Showing 10 of 1656 questions. Start a quiz to practice all questions with scoring and timer.

Practice All 1656 Questions →

More Mathematics Chapters

1 Sets Relations and Functions
1652 Qs →
2 Complex Numbers
1613 Qs →
3 Matrices and Determinants
1781 Qs →
4 Permutations and Combinations
1645 Qs →
5 Limits Continuity and Differentiability
1661 Qs →
6 Integral Calculus
1623 Qs →
7 Differential Equations
2044 Qs →
8 Coordinate Geometry
1290 Qs →

Other JEE Subjects

⚡ Physics → ⚗️ Chemistry →

Area Under Curves — JEE Mathematics Practice Questions Online

This page contains 1656 practice MCQs for the chapter Area Under Curves in JEE Mathematics. The questions are organized by difficulty — 333 easy, 722 medium, 601 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.