HOT PRACTICE TEST
Chapter 7 – Integrals
Class XII Mathematics • 25 Marks
Area Under a Curve
Section A – 6 × 1 = 6
1. Find ∫x dx.
2. Find ∫1/x dx.
3. State the fundamental idea of a definite integral.
4. Evaluate ∫₀¹ x dx.
5. Find ∫eˣ dx.
6. Does an indefinite integral contain an arbitrary constant?
Section B – 3 × 2 = 6
1. Evaluate ∫(2x+3)dx.
2. Evaluate ∫₀² x²dx.
3. Using substitution, evaluate ∫2x(x²+1)³dx.
Section C – 3 × 3 = 9
1. Evaluate ∫x sin x dx using integration by parts.
2. Evaluate ∫₀^(π/2) sin²x dx.
3. Evaluate ∫dx/(x²+4) using a standard result.
Section D – 1 × 4 = 4
1. Evaluate ∫₀¹ x ln(1+x²)dx using a suitable substitution and explain why the substitution simplifies the integral.