alleryIntegration is the inverse process of:
- limit-taking
- differentiation
- multiplication
- exponentiation
Show answer and solution
Correct answer: B. differentiation
Integration (antidifferentiation) reverses differentiation.
AP Calculus AB Unit 6A: Indefinite Integrals & Fundamental Theorem — practice questions — page 2
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 31–60 of 84.
Integration is the inverse process of:Read the answer and worked solution →$\displaystyle\int x^n\,dx$ (for $n\neq -1$) equals:Read the answer and worked solution →$\displaystyle\int \cos x\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \frac{1}{x}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int e^x\,dx$ equals:Read the answer and worked solution →The arbitrary constant $C$ added in an indefinite integral is called the:Read the answer and worked solution →$\displaystyle\int x^2\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \sin x\,dx$ equals:Read the answer and worked solution →The value of $\displaystyle\int_0^1 x\,dx$ is:Read the answer and worked solution →$\displaystyle\int \sec^2 x\,dx$ equals:Read the answer and worked solution →The value of $\displaystyle\int_0^{\pi/2} \cos x\,dx$ is:Read the answer and worked solution →$\displaystyle\int 2x\,dx$ equals:Read the answer and worked solution →The technique used to integrate a product of two functions is called:Read the answer and worked solution →$\displaystyle\int \sec^2 x\,dx$ equals:Read the answer and worked solution →$\displaystyle\int x^n\,dx$ (where $n \ne -1$) equals:Read the answer and worked solution →$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{x^2 - a^2}\,dx$ (with $|x| > a > 0$) equals:Read the answer and worked solution →The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2$ is:Read the answer and worked solution →The number of arbitrary constants in the general solution of a differential equation of order $n$ is:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \dfrac{1}{\sqrt{1 - x^2}}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int \log x\,dx$ equals:Read the answer and worked solution →Using the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:Read the answer and worked solution →Using integration by parts, $\displaystyle\int x e^x\,dx$ equals:Read the answer and worked solution →To solve the homogeneous differential equation $\dfrac{dy}{dx} = \dfrac{x^2 + y^2}{xy}$, the appropriate substitution is:Read the answer and worked solution →Using partial fractions, $\displaystyle\int \dfrac{1}{(x-1)(x-2)}\,dx$ equals:Read the answer and worked solution →$\displaystyle\int_0^1 \dfrac{1}{1 + x^2}\, dx = ?$Read the answer and worked solution →$\displaystyle\int_0^2 [x]\, dx$ where $[x]$ is the greatest integer function:Read the answer and worked solution →$\displaystyle\int_0^\pi \sin x\, dx = ?$Read the answer and worked solution →If $f$ is **odd** on $[-a, a]$, then $\displaystyle\int_{-a}^{a} f(x)\, dx$ equals:Read the answer and worked solution →
Worked practice questions
$\displaystyle\int x^n\,dx$ (for $n\neq -1$) equals:
- $x^{n+1} + C$
- $\dfrac{x^{n-1}}{n-1} + C$
- $n x^{n-1} + C$
- $\dfrac{x^{n+1}}{n+1} + C$
Show answer and solution
Correct answer: D. $\dfrac{x^{n+1}}{n+1} + C$
By the power rule for integration, ∫xⁿ dx = x^{n+1}/(n+1) + C for n ≠ −1.
$\displaystyle\int \cos x\,dx$ equals:
- $-\cos x + C$
- $\cos x + C$
- $\sin x + C$
- $-\sin x + C$
Show answer and solution
Correct answer: C. $\sin x + C$
Since d/dx(sin x) = cos x, ∫cos x dx = sin x + C.
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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