Calculus · Practice

Fundamental Theorem of Calculus — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

Evaluate $\displaystyle\int_0^3 x^2 \, dx$ using the Fundamental Theorem.

Problem 2

Evaluate $\displaystyle\int_5^5 \sin x \, dx$ .

Problem 3

Evaluate $\displaystyle\int_0^{\ln 2} e^x \, dx$ .

Problem 4

Let $G(x) = \displaystyle\int_0^x t^2 \, dt$ . Find $G'(2)$ .

Problem 5

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

Problem 6

Let $F(x) = \displaystyle\int_0^x 2 \, dt$ . Find $F'(x)$ .

Problem 7

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

Problem 8

Evaluate $\displaystyle\int_3^0 x^2 \, dx$ .

Problem 9

Let $H(x) = \displaystyle\int_0^{x^2} 1 \, dt$ . Find $H'(1)$ .

Problem 10

Find the net area between $f(x) = x$ and the $x$ -axis on $[0, 1]$ .

Problem 11

Let $G(x) = \displaystyle\int_1^x t^2 \, dt$ . Find $G'(\!\sqrt{3})$ .