6.7 FTC & Evaluating Definite Integrals

FTC Part 2

∫[a to b] f(x) dx = F(b) − F(a), where F is any antiderivative of f. Find an antiderivative, evaluate at the upper and lower limits, and subtract.

Example

∫[0 to 2] 2x dx: an antiderivative is x², so the value is 2² − 0² = 4.

Key terms

FTC Part 2

∫[a to b] f dx = F(b) − F(a).

F

Any antiderivative of f (F' = f).

Method

Antiderivative, evaluate at limits, subtract.

Example

∫[0 to 2] 2x dx = 4.

Link

Connects definite integrals to antiderivatives.

Try an AP-style question

∫₁³ (2x + 1) dx = ?

1. 12
2. 10
3. 8
4. 7