91Ó°ÊÓ

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{-\infty}^{\infty} 2 x e^{-x^{2}} d x $$

In Exercises \(21-28,\) express the integrands as a sum of partial fractions and evaluate the integrals. $$ \int \frac{8 x^{2}+8 x+2}{\left(4 x^{2}+1\right)^{2}} d x $$

In Exercises \(15-26,\) estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than \(10^{-4}\) by ( a ) the Trapezoidal Rule and (b) Simpson's Rule. (The integrals in Exercises \(15-22\) are the integrals from Exercises \(1-8 .\) ) $$ \int_{0}^{3} \frac{1}{\sqrt{x+1}} d x $$

Evaluate the integrals in Exercises \(1-28\). $$ \int \frac{\left(1-x^{2}\right)^{1 / 2}}{x^{4}} d x $$

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int 10^{2 \theta} d \theta $$

Evaluate each integral in Exercises \(1-36\) by using a substitution to reduce it to standard form. $$ \int \frac{9 d u}{1+9 u^{2}} $$

Evaluate the integrals in Exercises \(1-34\) without using tables. $$ \int_{0}^{1} x \ln x d x $$

Use the table of integrals at the back of the book to evaluate the integrals. \(\int \frac{d s}{\left(9-s^{2}\right)^{2}}\)

In Exercises \(15-26,\) estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than \(10^{-4}\) by ( a ) the Trapezoidal Rule and (b) Simpson's Rule. (The integrals in Exercises \(15-22\) are the integrals from Exercises \(1-8 .\) ) $$ \int_{0}^{2} \sin (x+1) d x $$

Evaluate the integrals in Exercises \(23-32\). $$ \int_{0}^{\pi / 4} \sec ^{4} \theta d \theta $$