In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.
∫ from -1 to 1 of (-x ln|x| dx)
In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.
∫ from 1 to 2 of (dx / (x ln x))
Center of gravity: Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x = -pi/4 and x = pi/4.
Evaluate the integrals in Exercises 1–24 using integration by parts.
∫ x² sin(x) dx
The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.
∫₁^∞ dx / [x√(x² − 1)]
Evaluate the integrals in Exercises 51–56 by making a substitution (possibly trigonometric) and then applying a reduction formula.
∫ (from 0 to √3/2) dy / (1 - y²)^(5/2)
