91Ó°ÊÓ

Mean Value Theorem for Integrals Find or approximate all points at which the given function equals its average value an the given interval. $$f(x)=\frac{\pi}{4} \sin x \text { on }[0, \pi]$$

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus. $$\int_{-2}^{-1} x^{-3} d x$$

Definite integrals Use geometry (not Riemann sums) to evaluate the following definite integrals. Sketch a graph of the integrand. show the region in question, and interpret your result. $$\int_{0}^{4} \sqrt{16-x^{2}} d x$$

Riemann sums from tables Evaluate the left and right Riemann sums for \(f\) over the given interval for the given value of \(n.\) \(n=4 ;[0,2]\) $$\begin{array}{|c|c|c|c|c|c|}\hline x & 0 & 0.5 & 1 & 1.5 & 2 \\\\\hline f(x) & 5 & 3 & 2 & 1 & 1 \\\\\hline\end{array}$$

Mean Value Theorem for Integrals Find or approximate all points at which the given function equals its average value an the given interval. $$f(x)=1-|x| \text { on }[-1,1]$$

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating. $$\int \sin x \sec ^{8} x d x$$

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating. $$\int \frac{e^{2 x}}{e^{2 x}+1} d x$$

Definite integrals Use geometry (not Riemann sums) to evaluate the following definite integrals. Sketch a graph of the integrand. show the region in question, and interpret your result. $$\int_{-1}^{3} \sqrt{4-(x-1)^{2}} d x$$

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus. $$\int_{0}^{\pi}(1-\sin x) d x$$

Mean Value Theorem for Integrals Find or approximate all points at which the given function equals its average value an the given interval. $$f(x)=\frac{1}{x} \text { on }[1,4]$$