91Ó°ÊÓ

Evaluate the integrals $$ \int_{0}^{2} x(x-3) d x $$

Write the sums without sigma notation. Then evaluate them. $$ \sum_{k=1}^{2} \frac{6 k}{k+1} $$

Evaluate the indefinite integrals in Exercises \(1-16\) by using the given substitutions to reduce the integrals to standard form. $$\int 2(2 x+4)^{5} d x, \quad u=2 x+4$$

In Exercises \(1-4,\) use finite approximations to estimate the area under the graph of the function using a. a lower sum with two rectangles of equal width. b. a lower sum with four rectangles of equal width. c. an upper sum with two rectangles of equal width. d. an upper sum with four rectangles of equal width. $$f(x)=4-x^{2} \text { between } x=-2 \text { and } x=2$$

In Exercises \(1-4,\) use finite approximations to estimate the area under the graph of the function using a. a lower sum with two rectangles of equal width. b. a lower sum with four rectangles of equal width. c. an upper sum with two rectangles of equal width. d. an upper sum with four rectangles of equal width. $$f(x)=x^{3} \quad \text { between } \quad x=0 \quad \text {and} \quad x=1$$

Write the sums without sigma notation. Then evaluate them. $$ \sum_{k=1}^{3} \frac{k-1}{k} $$

Evaluate the indefinite integrals in Exercises \(1-16\) by using the given substitutions to reduce the integrals to standard form. $$\int 7 \sqrt{7 x-1} d x, \quad u=7 x-1$$

Evaluate the integrals $$ \int_{-1}^{1}\left(x^{2}-2 x+3\right) d x $$

Evaluate the integrals $$ \int_{-2}^{2} \frac{3}{(x+3)^{4}} d x $$

In Exercises \(1-4,\) use finite approximations to estimate the area under the graph of the function using a. a lower sum with two rectangles of equal width. b. a lower sum with four rectangles of equal width. c. an upper sum with two rectangles of equal width. d. an upper sum with four rectangles of equal width. $$f(x)=1 /x \quad \text {between} \quad x=1 \quad \text {and} \quad x=5$$