91Ó°ÊÓ

Evaluate the sums in Exercises \(19-32\) $$a,\sum_{k=1}^{10} k \quad \text { b. } \sum_{k=1}^{10} k^{2} \quad \text { c. } \sum_{k=1}^{10} k^{3}$$

In Exercises \(15-22,\) graph the integrands and use known area formulas to evaluate the integrals. $$ \int_{-2}^{1}|x| d x $$

Evaluate the integrals in Exercises \(17-50\) $$ \int 3 y \sqrt{7-3 y^{2}} d y $$

In Exercises \(15-22,\) graph the integrands and use known area formulas to evaluate the integrals. $$ \int_{-1}^{1}(1-|x|) d x $$

Evaluate the integrals in Exercises \(1-28\). $$\int_{-\sqrt{3}}^{\sqrt{3}}(t+1)\left(t^{2}+4\right) d t$$

Evaluate the sums in Exercises \(19-32\) $$a.\sum_{k=1}^{13} k \quad \text { b. } \sum_{k=1}^{13} k^{2} \quad \text { c. } \sum_{k=1}^{13} k^{3}$$

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

In Exercises \(15-22,\) graph the integrands and use known area formulas to evaluate the integrals. $$ \int_{-1}^{1}(2-|x|) d x $$

Inscribe a regular \(n\) -sided polygon inside a circle of radius 1 and compute the area of the polygon for the following values of \(n :\) $$ \begin{array}{l}{\text { a. } 4 \text { (square) } \quad \text { b. } 8 \text { (octagon) } \quad \text { c. } 16} \\ {\text { d. Compare the areas in parts (a), (b), and (c) with the area of the }} \\ {\text { circle. }}\end{array} $$

Evaluate the sums in Exercises \(19-32\) $$\sum_{k=1}^{7}(-2 k)$$