91Ó°ÊÓ

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. $$ \int_{\pi / 2}^{\pi} \sqrt{x} \sin x d x $$

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{-2}^{-1}\left(u-\frac{1}{u^{2}}\right) d u $$

Find the indefinite integral and check the result by differentiation. $$ \int x\left(4 x^{2}+3\right)^{3} d x $$

Complete the table. Original Integral $$\int \frac{1}{(3 x)^{2}} d x$$

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{1}^{4} \frac{u-2}{\sqrt{u}} d u $$

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

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. $$ \int_{0}^{\sqrt{\pi / 2}} \cos x^{2} d x $$

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. $$ \int_{0}^{\sqrt{\pi / 4}} \tan x^{2} d x $$

Find the indefinite integral and check the result by differentiation. $$ \int t^{3} \sqrt{t^{4}+5} d t $$

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