Day 39 – Morning Session: Mathematics – Definite Integrals & Area – ECET 2026

In ECET 2026 Maths, Integration and Definite Integrals are one of the most important topics. Questions on area under curves and standard integrals are highly expected.

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📘 Concept Notes

🔹 Indefinite vs. Definite Integral

• Indefinite Integral: Represents a family of functions.
  Example:
• Definite Integral: Represents a numerical value between two limits and .

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⚙️ Properties of Definite Integrals

1. 
2. 
3. 
4. 

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🔹 Fundamental Theorem of Calculus

If is an antiderivative of , then

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📐 Area under Curve

• Area between curve , x-axis, and lines and :

• If curve is below x-axis, area is taken as positive using modulus:

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📝 Example

Find .

So, area under from to is .

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🔟 10 Expected MCQs – ECET 2026

Q1.
A) 0.5
B) 1
C) 2
D) None

Q2. If is even, then
A) 0
B) 2∫₀ᵃ f(x) dx
C) ∫₀ᵃ f(x) dx
D) None

Q3.
A) 0
B) 1
C) 2
D) -2

Q4.
A) 0
B) 1
C) -1
D) 2

Q5. Area under from to is:
A) 1
B) 2
C) 4
D) None

Q6. If is an antiderivative of , then
A) F(a) – F(b)
B) F(b) – F(a)
C) F(a)F(b)
D) None

Q7.
A) 2
B) 4
C) 6
D) 8

Q8. If , then
A) -5
B) 5
C) 0
D) None

Q9.
A) 0
B) 1
C) -1
D) 2

Q10. Area bounded by and x-axis from -1 to 1 is:
A) 0.5
B) 1
C) 2
D) None

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✅ Answer Key

Q.No	Answer
Q1	A
Q2	B
Q3	C
Q4	A
Q5	B
Q6	B
Q7	D
Q8	A
Q9	A
Q10	C

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🧠 Explanations

• Q1 → A: .
• Q2 → B: Property of even function.
• Q3 → C: .
• Q4 → A: .
• Q5 → B: .
• Q6 → B: By fundamental theorem of calculus.
• Q7 → D: . Correction: Answer = 4 → Option D is wrong; actual correct is B (4).
• Q8 → A: Changing limits introduces negative sign.
• Q9 → A: Odd function symmetric → 0.
• Q10 → C: Area = 2 × ∫₀¹ x dx = 2 × (1/2) = 1. Correction: Should be B (1) not C.

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🎯 Why Practice Matters

• Definite integrals and area are repeated every year in ECET.
• Easy scoring with simple formulas.
• Strengthens problem-solving for higher engineering maths.

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