Definite Integration — Practice Quiz
Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce
Try a 4-question quiz on Definite Integration for Maharashtra Board Class 12 Mathematics & Statistics -Commerce: tap an answer to check it and see why.
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Quick Quiz: Definite Integration
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Evaluate ∫₁³ 2x dx using the fundamental theorem of calculus.
Which property states that ∫ₐᵇ f(x) dx = -∫ᵇₐ f(x) dx?
Evaluate ∫₀² x² dx.
If f(x) is an even function, then ∫₋ₐᵃ f(x) dx equals:
Sample Questions
Which of the following are correct applications of definite integral properties?
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∫₂² f(x) dx = 0, ∫₁³ f(x) dx = ∫₁² f(x) dx + ∫₂³ f(x) dx, ∫₀¹ f(x) dx = ∫₀¹ f(t) dt
Property 1: Same limits give zero. Property 4: Split integration interval. Property 3: Dummy variable property. The last option is wrong due to Property 2 (sign change).
Evaluate ∫₀¹ (x + 1) dx.
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3/2
Step 1: ∫(x + 1) dx = x²/2 + x + c. Step 2: [x²/2 + x]₀¹ = (1/2 + 1) - (0 + 0) = 3/2. Split into ∫x dx + ∫1 dx for clarity.
What is ∫ₐᵃ 5x³ dx?
Which of the following integrals equal zero for odd functions?
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∫₋₃³ x³ dx, ∫₋₅⁵ sin x dx, ∫₋₂² x⁵ dx
For odd functions f(-x) = -f(x), ∫₋ₐᵃ f(x) dx = 0. x³, sin x, and x⁵ are odd functions. x² is even, so its integral over symmetric limits is non-zero.
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