The value of int_0^pi x * cos^2(x) dx correct to three decimal places (assuming that pi = 3.14) is ______.

Question

Accepted Answer

2.4649 (approximately 2.465 to three decimal places with pi = 3.14) We need to evaluate the definite integral of x*cos^2(x) over [0, pi]. The key trick is to use the power-reduction identity cos^2(x) = (1 + cos(2x))/2, which converts the integral into two manageable parts. The first part is a simple polynomial integral and the second uses integration by parts. With pi = 3.14, the answer is approximately 2.465.