Problem 17
Approximate the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of \(n\). (Round your answers to three significant digits.) $$ \int_{0}^{2} \sqrt{1+x^{3}} d x, n=4 $$
Problem 17
Use partial fractions to find the indefinite integral. $$ \int \frac{1}{2 x^{2}-x} d x $$
Problem 17
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{-\infty}^{0} e^{-x} d x $$
Problem 18
Use partial fractions to find the indefinite integral. $$ \int \frac{2}{x^{2}-2 x} d x $$
Problem 18
Find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int \frac{2 x}{e^{x}} d x $$
Problem 18
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{-\infty}^{-1} \frac{1}{x^{2}} d x $$
Problem 18
Approximate the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of \(n\). (Round your answers to three significant digits.) $$ \int_{0}^{1} \sqrt{1-x} d x, n=4 $$
Problem 19
Use partial fractions to find the indefinite integral. $$ \int \frac{10}{x^{2}-10 x} d x $$
Problem 19
Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{1}^{\infty} \frac{e^{\sqrt{x}}}{\sqrt{x}} d x $$
Problem 19
Approximate the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of \(n\). (Round your answers to three significant digits.) $$ \int_{0}^{1} \sqrt{1-x^{2}} d x, n=4 $$
