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Magazine Problem 4
$$\int x^{2} \sin x d x$$
Problem 4
Use the table of integrals at the back of the text to evaluate the integrals. $$\int \frac{x d x}{(2 x+3)^{3 / 2}}$$
Problem 4
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. $$\int_{-2}^{0}\left(x^{2}-1\right) d x$$
Problem 5
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. $$\int_{0}^{2}\left(t^{3}+t\right) d t$$
Problem 5
Use the table of integrals at the back of the text to evaluate the integrals. $$\int x \sqrt{2 x-3} d x$$
Problem 5
Evaluate the integrals $$\int \sin ^{3} x d x$$
Problem 5
Evaluate the integrals in Exercises \(1-14\). $$\int_{0}^{3 / 2} \frac{d x}{\sqrt{9-x^{2}}}$$
Problem 5
Evaluate the integrals without using tables. $$\int_{-1}^{1} \frac{d x}{x^{2 / 3}}$$
Problem 5
Evaluate the integrals using integration by parts. $$\int_{1}^{2} x \ln x d x$$
Problem 6
Use the table of integrals at the back of the text to evaluate the integrals. $$\int x(7 x+5)^{3 / 2} d x$$
