8.2 Evaluating Integrals of Polynomials, Trig and Exponentials

3 practice questionsNot yet reviewed

Notes

Use the basic antiderivative rules, then apply FTC Part 2.

Example: $\displaystyle \int_0^2 (3x^2 - 2x + 1)\,dx = \left[x^3 - x^2 + x\right]_0^2 = (8 - 4 + 2) - 0 = 6$.
$\displaystyle \int_0^\pi \sin x\,dx = \left[-\cos x\right]_0^\pi = 1 + 1 = 2$.
$\displaystyle \int_0^1 e^x\,dx = e - 1$ and $\displaystyle \int_1^e \frac{1}{x}\,dx = \ln e - \ln 1 = 1$.

Find $\displaystyle \int_0^2 (3x^2 - 2x + 1)\,dx$.

Find $\displaystyle \int_0^\pi \sin x\,dx$.

Find $\displaystyle \int_1^e \frac{1}{x}\,dx$.