Practice Fundamental Theorem of Calculus in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The theorem stating that differentiation and integration are inverse operations, linking antiderivatives to definite integrals.
Integration undoes differentiation. They're two sides of the same coin.
Example 1
easyLet G(x) = \int_0^x (t^2 + 1)\,dt. Find G'(x) using FTC Part 1.
Example 2
hardLet H(x) = \int_1^{x^2} \cos t\,dt. Find H'(x).
Example 3
mediumUse FTC Part 2 to evaluate \int_1^e \frac{1}{t}\,dt.
Example 4
mediumIf F(x) = \int_0^x e^{t^2}\,dt, find F'(x).