91Ó°ÊÓ

Use the Exponential Rule to find the indefinite integral. $$ \int 3(x-4) e^{x^{2}-8 x} d x $$

The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. $$ \int_{-4}^{0}\left[(x-6)-\left(x^{2}+5 x-6\right)\right] d x $$

Use the Midpoint Rule with \(n=4\) to approximate the area of the region bounded by the graph of \(f\) and the \(x\) -axis over the interval. Compare your result with the exact area. Sketch the region. $$ f(x)=3 x^{2}+1 \quad[-1,3] $$

Find the indefinite integral and check the result by differentiation. $$ \int\left(x^{2}-1\right)^{3}(2 x) d x $$

Find the indefinite integral and check your result by differentiation. $$ \int-4 d x $$

Use the Midpoint Rule with \(n=4\) to approximate the area of the region bounded by the graph of \(f\) and the \(x\) -axis over the interval. Compare your result with the exact area. Sketch the region. $$ f(x)=2 x-x^{3} $$

Use the Exponential Rule to find the indefinite integral. $$ \int 5 e^{2-x} d x $$

Sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. $$ \int_{-3}^{3} \sqrt{9-x^{2}} d x $$

Find the indefinite integral and check your result by differentiation. $$ \int 5 t^{2} d t $$

Find the indefinite integral and check the result by differentiation. $$ \int \sqrt{4 x^{2}-5}(8 x) d x $$