Textbook Question
Use any method to evaluate the integrals in Exercises 65–70.
∫ x cos³(x) dx
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Use any method to evaluate the integrals in Exercises 65–70.
∫ x cos³(x) dx
Evaluate the integrals in Exercises 1–22.
∫₀^(π/6) 3cos⁵(3x) dx
Use any method to evaluate the integrals in Exercises 55–66.
∫ 2 / (x(ln x - 2)³) dx
Annual rainfall The annual rainfall in inches for San Francisco, California, is approximately a normal random variable with mean 20.11 in. and standard deviation 4.7 in. What is the probability that next year’s rainfall will exceed 17 in.?
Evaluate the integrals in Exercises 1–24 using integration by parts.
∫x e^(3x) dx
In Exercises 67–73, use integration by parts to establish the reduction formula.
∫ x^n sin(x) dx = -x^n cos(x) + n ∫ x^(n-1) cos(x) dx