AP Calculus BC / Unit 6: Integration and Accumulation of Change

6.7 The Fundamental Theorem of Calculus and Definite Integrals

3 practice questions

Notes

If $F'=f$, then $$\int_a^b f(x)\,dx=F(b)-F(a)$$

Also: $\displaystyle f(b)=f(a)+\int_a^b f'(x)\,dx$ (net change).

Practice

$\displaystyle \int_1^3 2x\,dx=$

$f(2)=5$ and $\displaystyle \int_2^6 f'(x)dx=7$. Find $f(6)$.

$\displaystyle \int_0^{\pi}\sin x\,dx=$

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