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Magazine Problem 1
Evaluate the integrals in Exercises \(1-14\). $$\int \frac{d x}{\sqrt{9+x^{2}}}$$
Problem 1
Evaluate the integrals without using tables. $$\int_{0}^{\infty} \frac{d x}{x^{2}+1}$$
Problem 1
Evaluate the integrals using integration by parts. $$\int x \sin \frac{x}{2} d x$$
Problem 1
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. $$\int_{1}^{2} x d x$$
Problem 1
Evaluate the integrals $$\int \cos 2 x \, d x$$
Problem 2
Evaluate the integrals in Exercises \(1-14\). $$\int \frac{3 d x}{\sqrt{1+9 x^{2}}}$$
Problem 2
Use the table of integrals at the back of the text to evaluate the integrals. $$\int \frac{d x}{x \sqrt{x+4}}$$
Problem 2
Evaluate the integrals $$\int_{0}^{\pi} 3 \sin \frac{x}{3} d x$$
Problem 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. $$\int_{1}^{5}(2 x-1) d x$$
Problem 2
Evaluate the integrals without using tables. $$\int_{1}^{\infty} \frac{d x}{x^{1.001}}$$
