Evaluate the integrals in Exercises 1–8 using integration by parts.
∫ x sin(x) cos(x) dx

You are planning to use Simpson’s Rule to estimate the value of the integral Estimate ∫ from 1 to 2 of f(x) dx with an error magnitude less than 10⁻⁵ using Simpson’s Rule.

You have determined that |f⁽⁴⁾(x)| ≤ 3 throughout the interval of integration. How many subintervals should you use to ensure the required accuracy?

(Remember that for Simpson’s Rule the number of subintervals must be even.)

Evaluate the integrals in Exercises 37–44.

∫ cos⁵(x) sin⁵(x) dx

Which of the improper integrals in Exercises 63–68 converge and which diverge?

∫ from 1 to ∞ of ((ln z) / z) dz

Evaluate the integrals in Exercises 37–44.

∫ sec²(θ) sin³(θ) dθ

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫₋₁⁰ e^x / (e^x + e^(−x)) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ sin(2θ) dθ / (1 + cos(2θ))²