Question

二重积分问题，该怎么积分

二重积分问题，该怎么积分先积y后积x，积y该怎么做

Answer 1

∫∫ (sinx)/x dxdy
= ∫(0→1) dx ∫(x²→x) (sinx)/x dy
= ∫(0→1) (sinx)/x * (x - x²) dx
= ∫(0→1) (1 - x)sinx dx
= ∫(0→1) (x - 1) d(cosx)
= (x - 1)cosx：(0→1) - ∫(0→1) cosx d(x - 1)
= - (- 1)(1) - sinx：(0→1)
= 1 - sin(1)