The integral of the function y=∫xcos(x)dx is found using integration by parts, resulting in y = ∫xcos(x)dx is xsinx + cosx.
The integral in the question is integral of xcos(x)dx.
To solve this, we can use integration by parts, where one function is 'u' and the other is 'dv'. We choose u = x and dv = cos(x)dx.
Differentiating u, we get du = dx, and integrating dv, we get v = sin(x). Integration by parts formula is ∫udv = uv - ∫vdu.
Applying this, we get:
∫xcos(x)dx = x*sin(x) - ∫sin(x)*dx = xsin(x) + cos(x) + C, where C is the constant of integration.
Thus, the integral of the function y = ∫xcos(x)dx is xsinx + cosx.