Indefinite integral of xⁿ (n ≠ -1):
Axⁿ⁺¹/(n+1) + C
Bxⁿ⁻¹/n
Cn xⁿ⁻¹
Dxⁿ
Answer & Solution
Correct answer: A. xⁿ⁺¹/(n+1) + C
∫ xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1).
Reverse of power rule for differentiation.
For n = -1: ∫ x⁻¹ dx = ln|x| + C.
Keep practising Unit 6B: Definite Integration & Riemann Sums
Browse all Unit 6B: Definite Integration & Riemann Sums questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
∫ from 0 to π/2 sin x cos x dx =For ∫ dx / sqrt(a² - x²), let x = a sin θ. Result:∫ from 0 to 2 (x² - 2x) dx =Reduction formula example: ∫ sinⁿ x dx (for n ≥ 2) =∫ from 1 to e (1/x) dx =∫ x ln x dx (integration by parts: u = ln x, dv = x dx):∫ from 0 to ∞ e^(-x) dx =Area under y = x² from x = 0 to x = 2: