91Ó°ÊÓ

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$\int \frac{e^{-\cot z}}{\sin ^{2} z} d z$$

Evaluate the integrals without using tables. $$\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}$$

Evaluate the integrals. \(\int \sqrt{25-t^{2}} d t\)

The instructions for the integrals have two parts, one for the Trapezoidal Rule and one for Simpson's Rule. I. Using the Trapezoidal Rule a. Estimate the integral with \(n=4\) steps and find an upper bound for \(\left|E_{T}\right|\) b. Evaluate the integral directly and find \(\left|E_{T}\right|\) c. Use the formula \(\left(\left|E_{T}\right| /(\text { true value })\right) \times 100\) to express \(\left|E_{T}\right|\) as a percentage of the integral's true value. II. Using Simpson's Rule a. Estimate the integral with \(n=4\) steps and find an upper bound for \(\left|E_{S}\right|\) b. Evaluate the integral directly and find \(\left|E_{S}\right|\) c. Use the formula \(\left(\left|E_{S}\right| /(\text { true value })\right) \times 100\) to express \(\left|E_{S}\right|\) as a percentage of the integral's true value. $$\int_{1}^{2} \frac{1}{s^{2}} d s$$

Expand the quotients by partial fractions. $$\frac{t^{2}+8}{t^{2}-5 t+6}$$

Use the table of integrals at the back of the book to evaluate the integrals. $$\int \frac{\sqrt{9-4 x}}{x^{2}} d x$$

Evaluate the integrals using integration by parts. $$\int x e^{3 x} d x$$

Evaluate the integrals. $$\int_{0}^{\pi} \sin ^{5} \frac{x}{2} d x$$

Evaluate the integrals. \(\int \sqrt{1-9 t^{2}} d t\)

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$\int \frac{2^{\ln z^{3}}}{16 z} d z$$