Exam 13: Integral Calculus

Solve the problem. -A certain object moves in such a way that its velocity (in $\mathrm{m} / \mathrm{s}$ ) after time $\mathrm{t}$ (in $\mathrm{s}$ ) is given by $v=t^{2}+3 t+10$ . Find the distance traveled during the first four seconds.

Find the given indefinite integral. State whether integration by substitution or integration by parts was used. - $\int x e^{x / 3} d x$

Evaluate the integral. - $\int_{1}^{4} x^{-(1 / 2)} d x$

Approximate the area under the curve and above the $x$ -axis using $n$ rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle. - $f(x)=2 x^{3}-1$ from $x=1$ to $x=6 ; n=5$

Find the area bounded by the given curves. - $y=\ln x$ and $y=x e^{x} ;[1,3]$

Find the given indefinite integral. - $\left.\int 2-7 \ln x\right) d x$

A student has a demand equation and a selling price. What kind of surplus can the student calculate with this information?