91Ó°ÊÓ

Find the areas of the regions enclosed by the lines and curves. $$ y=\sqrt{|x|} \text { and } 5 y=x+6 \quad \text {(How many intersection points are there?)} $$

For the functions find a formula for the Riemann sum obtained by dividing the interval \([a, b]\) into \(n\) equal subintervals and using the right-hand endpoint for each \(c_{k} .\) Then take a limit of these sums as \(n \rightarrow \infty\) to calculate the area under the curve over \([a, b] .\) $$ f(x)=2 x^{3} \text { over the interval }[0,1]. $$

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

For the functions find a formula for the Riemann sum obtained by dividing the interval \([a, b]\) into \(n\) equal subintervals and using the right-hand endpoint for each \(c_{k} .\) Then take a limit of these sums as \(n \rightarrow \infty\) to calculate the area under the curve over \([a, b] .\) $$ f(x)=x^{2}-x^{3} \text { over the interval }[-1,0]. $$

Find the areas of the regions enclosed by the lines and curves. $$ y=\left|x^{2}-4\right| \quad \text { and } \quad y=\left(x^{2} / 2\right)+4 $$

Find the total area between the region and the \(x-\) axis. $$ y=x^{1 / 3}-x, \quad-1 \leq x \leq 8 $$

Evaluate the integrals in Exercises \(17-50\) $$ \int \frac{x}{(2 x-1)^{2 / 3}} d x $$

Find the areas of the regions enclosed by the lines and curves. $$ x=2 y^{2}, \quad x=0, \quad \text { and } \quad y=3 $$

Find the areas of the regions enclosed by the lines and curves. $$ x=y^{2} \quad \text { and } \quad x=y+2 $$

Find the areas of the regions enclosed by the lines and curves. $$ y^{2}-4 x=4 \quad \text { and } \quad 4 x-y=16 $$