91Ó°ÊÓ

Use the table of integrals at the back of the text to evaluate the integrals. $$\int \frac{d x}{x \sqrt{x+4}}$$

Expand the quotients in Exercises \(1-8\) by partial fractions. $$\frac{x+4}{(x+1)^{2}}$$

The instructions for the integrals in Exercises \(1-10\) 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 Simpsen'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. $$\int_{-1}^{1}\left(x^{2}+1\right) d x$$

Evaluate the integrals in Exercises \(1-14\). $$\int_{-2}^{2} \frac{d x}{4+x^{2}}$$

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

Evaluate the integrals $$\int \cos ^{3} x \sin x d x$$

Evaluate the integrals using integration by parts. $$\int t^{2} \cos t d t$$

Evaluate the integrals $$\int \sin ^{4} 2 x \cos 2 x d x$$

Evaluate the integrals without using tables. $$\int_{0}^{4} \frac{d x}{\sqrt{4-x}}$$

Use the table of integrals at the back of the text to evaluate the integrals. $$\int \frac{x d x}{(2 x+3)^{3 / 2}}$$