91Ó°ÊÓ

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{-1}^{1}(\sqrt[3]{t}-2) d t $$

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with \(n=4\). Compare these results with the approximation of the integral using a graphing utility. $$ \int_{1}^{1.1} \sin x^{2} d x $$

Find the indefinite integral and check the result by differentiation. $$ \int 5 x \sqrt[3]{1-x^{2}} d x $$

Find the indefinite integral and check the result by differentiation. $$ \int u^{2} \sqrt{u^{3}+2} d u $$

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with \(n=4\). Compare these results with the approximation of the integral using a graphing utility. $$ \int_{0}^{\pi / 2} \sqrt{1+\cos ^{2} x} d x $$

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{1}^{8} \sqrt{\frac{2}{x}} d x $$

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with \(n=4\). Compare these results with the approximation of the integral using a graphing utility. $$ \int_{0}^{\pi / 4} x \tan x d x $$

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

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{0}^{1} \frac{x-\sqrt{x}}{3} d x $$

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with \(n=4\). Compare these results with the approximation of the integral using a graphing utility. $$ \int_{0}^{\pi} f(x) d x, \quad f(x)=\left\\{\begin{array}{ll} \frac{\sin x}{x}, & x>0 \\ 1, & x=0 \end{array}\right. $$