91Ó°ÊÓ

Marginal Analysis Use a program similar to the simpson's Rule program on page 454 with \(n=4\) to approximate the change in revenue from the marginal revenue function \(d R / d x .\) In each case, assume that the number of units sold \(x\) increases from 14 to \(16 .\) $$ \frac{d R}{d x}=5 \sqrt{8000-x^{3}} $$

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$ \int_{0}^{1} \frac{1}{x^{2}} d x $$

find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int x(\ln x)^{2} d x $$

Use partial fractions to find the indefinite integral. $$ \int \frac{x+2}{x^{2}-4 x} d x $$

Use partial fractions to find the indefinite integral. $$ \int \frac{4 x^{2}+2 x-1}{x^{3}+x^{2}} d x $$

Marginal Analysis Use a program similar to the simpson's Rule program on page 454 with \(n=4\) to approximate the change in revenue from the marginal revenue function \(d R / d x .\) In each case, assume that the number of units sold \(x\) increases from 14 to \(16 .\) $$ \frac{d R}{d x}=50 \sqrt{x} \sqrt{20-x} $$

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$ \int_{0}^{1} \frac{1}{x} d x $$

find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int \ln 3 x d x $$

find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int \frac{(\ln x)^{2}}{x} d x $$

Use partial fractions to find the indefinite integral. $$ \int \frac{2 x-3}{(x-1)^{2}} d x $$