91Ó°ÊÓ

Calculate total cost (disregarding any fixed costs) or total profit. Total profit from marginal profit. A concert promoter sells \(x\) tickets and has a marginal-profit function given by $$P^{\prime}(x)=2 x-150$$ where \(P^{\prime}(x)\) is in dollars per ticket. This means that the rate of change of total profit with respect to the number of tickets sold, \(x\), is \(P^{\prime}(x)\). Find the total profit from the sale of the first 300 tickets.

Find the area under the given curve over the indicated interval. $$ y=4 ; \quad[1,3] $$

Find the area under the graph of \(f\) over [1,5]. $$ f(x)=\left\\{\begin{array}{ll} x+5, & \text { for } \quad x \leq 4 \\ 11-\frac{1}{2} x, & \text { for } \quad x>4 \end{array}\right. $$

Find each integral. $$ \int x^{7} d x $$

Find each integral. $$ \int 4 d x $$

Evaluate. (Be sure to check by differentiating!) $$ \int\left(3 t^{4}+2\right) t^{3} d t $$

Find each integral. $$ \int\left(2 t^{2}+5 t-3\right) d t $$

Evaluate. (Be sure to check by differentiating!) $$ \int t^{2} e^{-t^{3}} d t $$

Find the area of the region bounded by the graphs of the given equations. $$ y=3, y=x, x=0 $$

Use geometry to evaluate each definite integral. \(\int_{2}^{6} 3 d x\)