allery∫ x dx equals:
- ln x + C
- x²/2 + C
- x²
- 1
Show answer and solution
Correct answer: B. x²/2 + C
∫ xn dx = x^(n+1)/(n+1) + C for n ≠ -1. So ∫ x dx = x²/2 + C, where C is the constant of integration.
AP Calculus AB Unit 6A: Indefinite Integrals & Fundamental Theorem — practice questions
Explore 84 free Unit 6A: Indefinite Integrals & Fundamental Theorem questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 84.
∫ x dx equals:Read the answer and worked solution →∫ cos x dx equals:Read the answer and worked solution →∫ sin x dx equals:Read the answer and worked solution →∫ eˣ dx equals:Read the answer and worked solution →∫ dx/x for x > 0 equals:Read the answer and worked solution →∫ sec² x dx equals:Read the answer and worked solution →∫ (3x² - 4x + 5) dx equals:Read the answer and worked solution →Definite integral ∫₀¹ x² dx equals:Read the answer and worked solution →∫ sec x tan x dx equals:Read the answer and worked solution →By substitution u = x², ∫ 2x sin(x²) dx equals:Read the answer and worked solution →∫ dx/(1 + x²) equals:Read the answer and worked solution →∫ dx/√(1 - x²) equals:Read the answer and worked solution →∫ x eˣ dx (using integration by parts):Read the answer and worked solution →∫₀^(π/2) sin x dx equals:Read the answer and worked solution →∫ ln x dx (by parts):Read the answer and worked solution →∫₀¹ x e^(x²) dx equals:Read the answer and worked solution →∫ dx/(x ln x) equals:Read the answer and worked solution →∫ (x² + 1)/(x² - 1) dx equals:Read the answer and worked solution →∫ sin³ x dx (using sin³ x = sin x (1 - cos² x)):Read the answer and worked solution →∫ dx/√(x² + a²) equals:Read the answer and worked solution →∫ dx/(x² + 4) equals:Read the answer and worked solution →∫₀^(π) sin² x dx equals:Read the answer and worked solution →∫₋ₐ^a x³ dx equals (for any a):Read the answer and worked solution →∫ cosec² x dx equals:Read the answer and worked solution →By partial fractions, ∫ dx/(x(x+1)) equals:Read the answer and worked solution →∫₀^(2π) cos x dx equals:Read the answer and worked solution →Area under y = x² from x = 0 to x = 2:Read the answer and worked solution →∫ x sin x dx (by parts):Read the answer and worked solution →∫ dx/(a² - x²) (for |x| < a):Read the answer and worked solution →∫₀^(π/2) sin x cos x dx equals:Read the answer and worked solution →
Worked practice questions
∫ cos x dx equals:
- tan x + C
- -sin x + C
- sin x + C
- cos x + C
Show answer and solution
Correct answer: C. sin x + C
∫ cos x dx = sin x + C, since d/dx (sin x) = cos x.
∫ sin x dx equals:
- -cos x + C
- -sin x + C
- cos x + C
- sin x + C
Show answer and solution
Correct answer: A. -cos x + C
∫ sin x dx = -cos x + C, since d/dx (-cos x) = sin x.
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Practise Unit 6A: Indefinite Integrals & Fundamental Theorem →More Mathematics topics
Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits