91Ó°ÊÓ

In Problems 15-34, use the method of substitution to find each of the following indefinite integrals. \(\int \cos (3 x+2) d x\)

In Problems 17-26, find \(G^{\prime}(x)\). $$ G(x)=\int_{x}^{1} 2 t d t $$

In Problems 17-22, 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)= \begin{cases}3 x & \text { if } 0 \leq x \leq 1 \\ 2(x-1)+2 & \text { if } 1

In Problems 15-34, use the method of substitution to find each of the following indefinite integrals. \(\int \sin (2 x-4) d x\)

In Problems 17-22, 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)= \begin{cases}\sqrt{1-x^{2}} & \text { if } 0 \leq x \leq 1 \\ x-1 & \text { if } 1

In Problems 17-26, find \(G^{\prime}(x)\). $$ G(x)=\int_{0}^{x}\left(2 t^{2}+\sqrt{t}\right) d t $$

If a function \(f\) is increasing on \([a, b]\), will the left Riemann sum be larger or smaller than \(\int_{a}^{b} f(x) d x\) ?

In Problems 15-34, use the method of substitution to find each of the following indefinite integrals. \(\int \sin (6 x-7) d x\)

If a function \(f\) is increasing on \([a, b]\), will the right Riemann sum be larger or smaller than \(\int_{a}^{b} f(x) d x\) ?

In Problems 17-22, 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)= \begin{cases}-\sqrt{4-x^{2}} & \text { if }-2 \leq x \leq 0 \\ -2 x-2 & \text { if } 0