Final answer:
The value of the integral ∫ (0 to π) x sin(x) dx is calculated using integration by parts and the result is π.
Step-by-step explanation:
The question asks us to find the value of the integral of x sin(x) from 0 to π. This is a problem in calculus, specifically involving integration. We can solve this integral using integration by parts, which is based on the formula ∫ u dv = uv - ∫ v du.
Let's assign u = x, which means du = dx; dv = sin(x) dx, which means v = -cos(x). The integration by parts formula now gives us:
Hence, the value of the integral ∫ (0 to π) x sin(x) dx is π.