Question

Evaluate the iterated integral sin x dx dy. Jo Jy

Answer 1

Integral^pi_0 integral^pi_y sin x/x dx dy Since the integral integral sin x/x dx is too hard, we change order of integration, so that integrate with respect to y First the double integral is taken over a region R, which is defined by the inequalities 0 lessthanorequalto y lessthanorequalto pi, and y lessthanorequalto x lessthanorequalto pi Graphing this region it is clear that it is a triangle with vertices, (0, 0), (pi, 0) (pi, pi).. it is also defined by the inequalities, 0 lessthanorequalto x lessthanorequalto pi and 0 lessthanorequalto y lessthanorequalto x \r\n therefore integral^pi_0 integral^pi_y sin x/x dx dy = integral^pi_0 integral^x_0 sin x/x dy dx = integral^pi_0 sin x/x y]^x_0 dx = integral^pi_0 sin x dx = -cos x]^pi_0 = -cos pi + cos 0 = 1 + 1 = 2 ans) integral^pi_0 integral^pi_y sin x/x dx dy = 2 we change order of integration of integration to find the iterated integral Answer)2
we change order of integration to find the iterated integral

Answer)2