FAST-NU Advanced Mathematics — Integration
Integration is part of the Advanced Mathematics section of FAST's BS CS/Engineering admission test (usually 50 of the 120 MCQs, 50% of the marks). It breaks into 5 subtopics, and we hold 98 FAST-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (5)
How Integration is tested
Across the 7 FAST-pattern papers on ParhaiKrlo, Integration accounts for 35 questions. It appears in all 7, about 5 questions a paper. The heaviest was FAST Past Paper 07, with 5 questions.
| Paper | Questions |
|---|---|
| FAST Past Paper 07 | 5 |
| FAST Past Paper 06 | 5 |
| FAST Past Paper 05 | 5 |
| FAST Past Paper 04 | 5 |
| FAST Past Paper 03 | 5 |
| FAST Past Paper 02 | 5 |
| FAST Past Paper 01 | 5 |
Integration MCQs from the FAST-pattern papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · FAST Past Paper 07 · Integration
∫(1/x + sec² x) dx is equal to:
- A.ln|x| + tan x + C
- B.−1/x² + tan x + C
- C.ln|x| − cot x + C
- D.ln|x| + sec x tan x + C
Show answer
Answer: A. ln|x| + tan x + C — ∫(1/x) dx = ln|x| and ∫sec² x dx = tan x.
- Q2 · FAST Past Paper 06 · Integration
∫ 1/(1 + x²) dx is equal to:
- A.ln(1 + x²) + C
- B.sin⁻¹ x + C
- C.x + x³/3 + C
- D.tan⁻¹ x + C
Show answer
Answer: D. tan⁻¹ x + C — d/dx (tan⁻¹ x) = 1/(1 + x²), so the integral is tan⁻¹ x + C.
- Q3 · FAST Past Paper 05 · Integration
∫ sin x dx is equal to:
- A.−cos x + C
- B.cos x + C
- C.sin x + C
- D.−sin x + C
Show answer
Answer: A. −cos x + C — d/dx(−cos x) = sin x, so ∫ sin x dx = −cos x + C.