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Integration — JEE Practice

30 practice questions across 2 topics. Filter by difficulty, solve topic-wise MCQs, and review detailed solutions.

2 Topics30 Questions

Indefinite Integrals(15 Qs)

easy (5)

Q1∫xⁿ dx (n ≠ -1) =Q2∫cos x dx =Q3∫eˣ dx =Q4∫(1/x) dx =Q5∫sec²x dx =

medium (5)

Q1∫sin²x dx =Q2∫eˣ(f(x) + f'(x)) dx =Q3∫1/(x²+a²) dx =Q4∫1/√(a²-x²) dx =Q5Integration by parts formula is:

hard (5)

Q1∫x eˣ dx =Q2∫1/(x²-a²) dx =Q3∫√(a²-x²) dx =Q4∫dx/(1 + eˣ) =Q5∫tan x dx =

Definite Integrals & Area(15 Qs)

easy (5)

Q1∫₀¹ x² dx =Q2The fundamental theorem of calculus states ∫ₐᵇ f(x)dx =Q3∫₀^π sin x dx =Q4Area under y = f(x), x-axis, from a to b (f≥0) is:Q5∫₋₁¹ x³ dx =

medium (5)

Q1If f(x) is even, ∫₋ₐᵃ f(x)dx =Q2King's property: ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx. Using this, ∫₀^(π/2) sinx/(sinx+cosx) dx =Q3Area between y = x² and y = x from 0 to 1 is:Q4∫₀^(2π) |sin x| dx =Q5Leibniz rule: d/dx ∫₀ˣ f(t)dt =

hard (5)

Q1Wallis formula: ∫₀^(π/2) sin^n(x) dx for n even = (n-1)!!/(n!!)) · π/2. For n=4:Q2Area enclosed by ellipse x²/a² + y²/b² = 1 is:Q3∫₀^∞ e⁻ˣ dx =Q4The integral ∫₀¹ ln(x) dx =Q5Volume of revolution of y = f(x) about x-axis from a to b (disc method) is:

More Mathematics Chapters

Sets, Relations & Functions

15 Qs

Complex Numbers

15 Qs

Quadratic Equations

15 Qs

Permutations & Combinations

15 Qs

Binomial Theorem

15 Qs

Matrices & Determinants

15 Qs

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