91Ó°ÊÓ

Calculate \(\int_{a}^{b} f(x) d x\), where a and \(b\) are the left and right end points for which f is defined, by using the Interval Additive Property and the appropriate area formulas from plane geometry. Begin by graphing the given function. $$ f(x)=\left\\{\begin{array}{ll} \sqrt{1-x^{2}} & \text { if } 0 \leq x \leq 1 \\ x-1 & \text { if } 1

Find \(G^{\prime}(x)\). $$ G(x)=\int_{0}^{x}\left(2 t^{2}+\sqrt{t}\right) d t $$

Find all values of \(c\) that satisfy the Mean Value Theorem for Integrals on the given interval. $$ f(x)=|x| ; \quad[-2,2] $$

Calculate \(\int_{a}^{b} f(x) d x\), where a and \(b\) are the left and right end points for which f is defined, by using the Interval Additive Property and the appropriate area formulas from plane geometry. Begin by graphing the given function. $$ f(x)=\left\\{\begin{array}{ll} -\sqrt{4-x^{2}} & \text { if }-2 \leq x \leq 0 \\ -2 x-2 & \text { if } 0

Find \(G^{\prime}(x)\). $$ G(x)=\int_{1}^{x} \cos ^{3} 2 t \tan t d t ;-\pi / 2

Use Special Sum Formulas 1-4 to find each sum. $$ \sum_{i=1}^{10}[(i-1)(4 i+3)] $$

use the method of substitution to find each of the following indefinite integrals. $$ \int \cos (\pi v-\sqrt{7}) d v $$

use the method of substitution to find each of the following indefinite integrals. $$ \int x \sqrt{x^{2}+4} d x $$

Find all values of \(c\) that satisfy the Mean Value Theorem for Integrals on the given interval. $$ H(z)=\sin z ; \quad[-\pi, \pi] $$

Calculate \(\int_{a}^{b} f(x) d x\), where a and \(b\) are the left and right end points for which f is defined, by using the Interval Additive Property and the appropriate area formulas from plane geometry. Begin by graphing the given function. $$ f(x)=\sqrt{A^{2}-x^{2}} ;-A \leq x \leq A $$