Integration is one of the most important topics in Engineering Mathematics. Almost every year 2–3 direct questions come from basic integration rules and formulas.
⚙️ Concept Notes – Integration Basics
- Integration is the reverse process of differentiation.
- Represents the area under a curve.
- Symbol: ∫ f(x) dx
If
then,
where C = constant of integration.
⚙️ Basic Rules of Integration
- Constant Rule
Power Rule (n ≠ –1)
Sum/Difference Rule
Constant Multiple Rule
⚙️ Standard Integration Formulas
🌟 Examples
Ex 1:
Ex 2:
Ex 3:
🔟 10 Expected MCQs – ECET 2026
Q1. ∫ 5 dx = ?
A) 5x + C
B) 5 + C
C) x + 5
D) None
Q2. ∫ x² dx = ?
A) x³ + C
B) x³/3 + C
C) 2x + C
D) None
Q3. ∫ 1/x dx = ?
A) x
B) log(x) + C
C) ln|x| + C
D) None
Q4. ∫ sin x dx = ?
A) cos x + C
B) –cos x + C
C) tan x + C
D) None
Q5. ∫ cos x dx = ?
A) –sin x + C
B) sin x + C
C) tan⁻¹x + C
D) None
Q6. ∫ e^x dx = ?
A) e^x + C
B) ln|x| + C
C) x + C
D) None
Q7. ∫ sec²x dx = ?
A) –cot x + C
B) cos x + C
C) tan x + C
D) None
Q8. ∫ (3x² + 2x) dx = ?
A) x³ + x² + C
B) x³ + x²/2 + C
C) x³ + x² + C
D) None
Q9. ∫ 1/(1 + x²) dx = ?
A) tan⁻¹x + C
B) cos⁻¹x + C
C) log(1+x²)
D) None
Q10. ∫ 1/√(1–x²) dx = ?
A) tan⁻¹x + C
B) cos⁻¹x + C
C) sin⁻¹x + C
D) None
✅ Answer Key
| Q.No | Answer |
|---|---|
| Q1 | A |
| Q2 | B |
| Q3 | C |
| Q4 | B |
| Q5 | B |
| Q6 | A |
| Q7 | C |
| Q8 | C |
| Q9 | A |
| Q10 | C |
🧠 Explanations
- Q1: Constant rule → ∫k dx = kx + C
- Q2: Power rule → ∫ x² dx = x³/3 + C
- Q3: ∫ 1/x dx = ln|x| + C
- Q4: ∫ sin x dx = –cos x + C
- Q5: ∫ cos x dx = sin x + C
- Q6: ∫ e^x dx = e^x + C
- Q7: ∫ sec²x dx = tan x + C
- Q8: ∫ (3x² + 2x) dx = x³ + x² + C
- Q9: ∫ 1/(1+x²) dx = tan⁻¹x + C
- Q10: ∫ 1/√(1–x²) dx = sin⁻¹x + C
🎯 Why Practice Matters
Integration basics are formula-based and compulsory in ECET.
Just by remembering these formulas, you can secure 2–3 marks easily.
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