Definite Integrals & Properties
Maths Higher · Grade 12 · Week 23 · 25 questions
This Grade 12 mathematics chapter on Definite Integrals & Properties is high-yield for CBSE + JEE, exploring core concepts. Board paper almost always contains one 5-mark proof and two 3-mark application problems from this area.
What you'll practise
- Master the key derivations and worked examples from NCERT for definite integrals & properties
- Solve CBSE board-pattern problems from definite integrals & properties including NCERT exemplar-level questions
All 25 questions in this Definite Integrals & Properties quiz
Grade 12 Maths Higher — Definite Integrals & Properties: 25 practice questions with instant scoring and explanations.
- Definite integral ∫_a^b f(x)dx represents:
- Fundamental Theorem of Calculus: ∫_a^b f(x)dx =
- Using the standard identity, the value of ∫_a^a f(x)dx is:
- ∫_a^b f(x)dx + ∫_b^c f(x)dx =
- ∫_a^b f(x)dx = -∫_b^a f(x)dx is:
- ∫_a^b k·f(x)dx = (k is constant)
- ∫_a^b (f(x) + g(x))dx =
- If f(x) ≥ 0 on [a,b], then ∫_a^b f(x)dx:
- If f(x) ≥ g(x) on [a,b], then:
- Mean Value Theorem for Integrals: ∫_a^b f(x)dx =
- ∫_0^π sin(x)dx =
- ∫_0^π cos(x)dx =
- Using the standard identity, the value of ∫_0^1 x^n dx is:
- ∫_0^∞ e^(-x)dx =
- If f is even, ∫_(-a)^a f(x)dx =
- If f is odd, ∫_(-a)^a f(x)dx =
- ∫_1^e ln(x)dx =
- Cauchy-Schwarz inequality for integrals: (∫f·g)² ≤
- For substitution in definite integrals ∫_a^b f(g(x))g'(x)dx with u = g(x):
- ∫_0^(π/2) sin²(x)dx =
- ∫_0^(π/2) cos²(x)dx =
- Wallis formula ∫_0^(π/2) sin^n(x)dx uses:
- Leibniz rule for differentiating under integral sign d/da[∫_a^b f(x,a)dx] =
- For improper integrals ∫_a^∞ f(x)dx, we evaluate as:
- ∫₀^π sin x dx equals:
Question 1 of 250 correct so far