91Ó°ÊÓ

Calculate total cost, disregarding any fixed costs. Total cost from marginal cost. Redline Roasting has found that the cost, in dollars per pound, of the coffee it roasts is $$ C^{\prime}(x)=-0.012 x+6.50, \quad \text { for } x \leq 300 $$ where \(x\) is the number of pounds of coffee roasted. Find the total cost of roasting 200 lb of coffee.

Evaluate. Assume \(u>0\) when In \(u\) appears. (Be sure to check by differentiating!) $$\int\left(8+x^{3}\right)^{5} 3 x^{2} d x$$

Determine these indefinite integrals. $$\int x^{6} d x$$

Find the area under the graph of fover the interval [1,5] $$f(x)=\left\\{\begin{array}{lll} 2 x+1, & \text { for } & x \leq 3 \\ 10-x, & \text { for } & x > 3 \end{array}\right.$$

Evaluate using integration by parts or substitution. Check by differentiating. $$\int 4 x e^{4 x} d x$$

Evaluate. Assume \(u>0\) when In \(u\) appears. (Be sure to check by differentiating!) $$\int\left(x^{2}-7\right)^{6} 2 x d x$$

Graph each of the following equations. Equations must be solved for \(y\) before they can be entered into most calculators. Graphicus does not require that equations be solved for \(y\). $$f(x)=\left\\{\begin{array}{lll} x+5, & \text { for } & x \leq 4 \\ 11-\frac{1}{2} x, & \text { for } & x > 4 \end{array}\right.$$

Determine these indefinite integrals. $$\int x^{7} d x$$

Evaluate using integration by parts or substitution. Check by differentiating. $$\int 3 x e^{3 x} d x$$

Evaluate using integration by parts or substitution. Check by differentiating. $$\int x^{3}\left(3 x^{2}\right) d x$$