Integration

Work on antiderivatives, definite integrals, and theorem-based integration questions.

Focus points

✓Recognize standard antiderivative forms quickly.

✓Keep constant-of-integration habits consistent.

✓Link definite integrals to area and accumulation.

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

Practice set

Question lineup

Mark each one done as you go — finish them all to claim your chips.

6 revision prompts

Question 1OpenStax Calculus Volume 1, Sec. 4.10 Checkpoint 4.49

Find all antiderivatives of f (x) = \sin x .

Question 2OpenStax Calculus Volume 1, Sec. 4.10 Example 4.52(1)

Evaluate \int (5 x^{3} - 7 x^{2} + 3 x + 4) d x .

Question 3OpenStax Calculus Volume 1, Sec. 4.10 Example 4.52(2)

Evaluate \int \frac{x^{2} + 4 \sqrt[3]{x}}{x} d x .

Question 4OpenStax Calculus Volume 1, Sec. 4.10 Example 4.52(3)

Evaluate \int \frac{4}{1 + x^{2}} d x .

Question 5OpenStax Calculus Volume 1, Sec. 5.2 Exercises, 337

Evaluate \int_{0}^{2} (3 x + 1) d x .

Question 6OpenStax Calculus Volume 1, Sec. 5.4 Exercises, 393

Find \frac{d}{d x} \int_{1}^{x} t^{4} d t .