ECAT Mathematics — Integration
Integration is part of the Mathematics section of the UET ECAT (30 of the 100 MCQs). It breaks into 6 subtopics, and we hold 52 ECAT-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (6)
How Integration is tested
Across the 7 ECAT past papers on ParhaiKrlo, Integration accounts for 21 questions. It appears in all 7, about 3 questions a paper. The heaviest was ECAT Past Paper 06, with 5 questions, and the most recent is ECAT Past Paper 07, with 3.
| Paper | Questions |
|---|---|
| ECAT Past Paper 07 | 3 |
| ECAT Past Paper 06 | 5 |
| ECAT Past Paper 05 | 4 |
| ECAT Past Paper 04 | 2 |
| ECAT Past Paper 03 | 2 |
| ECAT Past Paper 02 | 2 |
| ECAT Past Paper 01 | 3 |
Integration MCQs from the ECAT past papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · ECAT Past Paper 07 · Integration
The solution of the differential equation x dy + (y − 1) dx = 0 is:
- A.ln[x + (y − 1)] = 0
- B.x(y − 1) = c
- C.x e^(y − 1) = c
- D.xy + x(y − 1) = c
Show answer
Answer: B. x(y − 1) = c — dy/(y − 1) = −dx/x → ln(y − 1) + ln x = ln c → x(y − 1) = c.
- Q2 · ECAT Past Paper 06 · Integration
If dy/dx = x³ + 3, then y is given by:
- A.y = x⁴/4 + 3x + c
- B.y = 3x² + c
- C.y = 3x² + 3 + c
- D.y = x³/3 + x + c
Show answer
Answer: A. y = x⁴/4 + 3x + c — Integrate term by term: ∫x³ dx = x⁴/4, ∫3 dx = 3x.
- Q3 · ECAT Past Paper 05 · Integration
The area enclosed by y = cos x and the x-axis from x = 0 to x = π/2 is equal to:
- A.∫ from π/2 to π of sin x dx
- B.∫ from 0 to π/2 of (−sin x) dx
- C.∫ from 0 to π of cos x dx
- D.∫ from 0 to π of sin x dx
Show answer
Answer: A. ∫ from π/2 to π of sin x dx — The required area is ∫₀^(π/2) cos x dx = 1, and ∫ from π/2 to π of sin x dx = −cos π + cos(π/2) = 1 as well.