Account Sign in Sign up

← All lessons

Integrals (Foundations)

Core skills for this exam family.

Phase 2 · AP Calculus

Foundations Standard Advanced

Integrals: core idea

\int x^n\,dx=\frac{x^{n+1}}{n+1}+C

.

Example problem: hint and answer

Evaluate $\int_0^1 2x\,dx$ .

Hint: Power rule. Answer: 1.

Practice (9 problems — type your answers)

1. Evaluate $\int_0^{\pi}\sin x\,dx$ .
2. Evaluate $\int_1^e \dfrac{dx}{x}$ .
3. Evaluate $\int_0^2 1\,dx$ .
4. Evaluate $\int_{-1}^1 x\,dx$ .
5. Evaluate $\int_0^1 x^2\,dx$ .
6. Antiderivative of $3x^2$ evaluated difference $F(2)-F(0)$ ?
7. Evaluate $\int_0^{\pi/2}\cos x\,dx$ .
8. Evaluate $\int_1^4 x^{-1/2}\,dx$ .
9. Evaluate $\int_0^1 e^x\,dx$ .

Integrals Practice Problems — Foundations