If ∫xeˣdx=eˣ(x−1)+C, then ∫₀¹xeˣdx equals:
- 0
- 1
- e−1
- 1−e
Show answer and explanation
Answer: B. 1
[eˣ(x−1)]₀¹ = 0−(−1) = 1.
FSC Mathematics: Integration, questions with answers
Practise 39 real Federal Board questions on Integration from 2023 to 2026. See the answer and explanation as soon as you answer.
39real questions
15multiple choice
5exam sessions
About Integration in FSC Mathematics
Integration is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (12th class), and about 8% of its real questions come from it. Tayyari Karo has 39 real questions on this chapter from 2023 to 2026; 15 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 18 medium, 12 hard, 9 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
Average value of f(x)=x² on [0,3] is:
- 6
- 5
- 4
- 3
Show answer and explanation
Answer: D. 3
(1/3)∫₀³x²dx=(1/3)(9)=3.
If 2∫₀³xdx=2k−3, then the value of 'k' is:
- 2
- 3
- 4
- 6
Show answer and explanation
Answer: D. 6
2×(9/2)=9=2k−3 ⇒ k=6.
What evaluates ∫₀^(π/2) Cosx·e^(Sinx) dx?
- 2e
- e
- e+1
- e−1
Show answer and explanation
Answer: D. e−1
Let u=Sinx, du=Cosx dx. ∫₀¹eᵘdu = e¹−e⁰ = e−1.
If 2∫₀²(x−k)dx=1, then what is the value of k?
- 3/4
- 4/3
- 1/2
- 3/2
Show answer and explanation
Answer: A. 3/4
∫₀²(x−k)dx = 2−2k. Setting 2(2−2k)=1 gives 4−4k=1, so k=3/4.
∫₋₁¹ (x + |x|) dx = ...
- −1
- 0
- 1
- 2
Show answer and explanation
Answer: C. 1
∫₋₁¹x dx = 0 (odd function). ∫₋₁¹|x|dx = 2∫₀¹x dx = 1. Sum = 0+1 = 1.
Evaluate ∫sin²x dx
Show model answer
sin²x = (1−cos2x)/2
∫(1−cos2x)/2 dx = x/2 − sin2x/4 + C
= x/2 − (sin2x)/4 + C
Evaluate ∫dx/[x²√(x²−9)]
Show model answer
Standard result: ∫dx/[x²√(x²−a²)] = √(x²−a²)/(a²x) + c, with a=3
= √(x²−9)/(9x) + c
Sessions with Integration questions
| Session | Questions |
|---|---|
| 2026 Annual | 8 |
| 2025 1st Annual | 9 |
| 2025 2nd Annual | 5 |
| 2024 Annual | 8 |
| 2023 Annual | 9 |
Common questions
What does the Integration chapter cover on this page?
39 real Federal Board (FBISE) Mathematics questions on Integration from 2023 to 2026, for 12th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Conic Sections 46
- Vectors 46
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Binomial Theorem 20
- Permutation/Combination/Probability 19
- Number Systems 17