91Ó°ÊÓ

Evaluate the integrals in Exercises \(13-48\) . $$ \int \frac{6 \cos t}{(2+\sin t)^{3}} d t $$

For the functions in Exercises \(35-40\) find a formula for the upper sum obtained by dividing the interval \([a, b]\) into \(n\) equal subintervals. Then take a limit of these sums as \(n \rightarrow \infty\) to calculate the area under the curve over \([a, b]\). $$ f(x)=2 x \text { over the interval }[0,3] $$

In Exercises \(37-42,\) find the total area between the region and the \(x\) -axis. $$ y=-x^{2}-2 x, \quad-3 \leq x \leq 2 $$

Evaluate the integrals in Exercises \(13-48\) . $$ \int \sqrt{\cot y} \csc ^{2} y d y $$

Evaluate the integrals in Exercises \(13-48\) . $$ \int \frac{\sec z \tan z}{\sqrt{\sec z}} d z $$

For the functions in Exercises \(35-40\) find a formula for the upper sum obtained by dividing the interval \([a, b]\) into \(n\) equal subintervals. Then take a limit of these sums as \(n \rightarrow \infty\) to calculate the area under the curve over \([a, b]\). $$ f(x)=3 x^{2} \text { over the interval }[0,1] $$

In Exercises \(37-42,\) find the total area between the region and the \(x\) -axis. $$ y=3 x^{2}-3, \quad-2 \leq x \leq 2 $$

Evaluate the integrals in Exercises \(13-48\) . $$ \int \frac{1}{t^{2}} \cos \left(\frac{1}{t}-1\right) d t $$

In Exercises \(37-42,\) find the total area between the region and the \(x\) -axis. $$ y=x^{3}-3 x^{2}+2 x, \quad 0 \leq x \leq 2 $$

Evaluate the integrals in Exercises \(13-48\) . $$ \int \frac{1}{\sqrt{t}} \cos (\sqrt{t}+3) d t $$