Question

Find the value of ∫∫ xydxdy over the area bpunded by parabola y=x^2 and x = -y^2, is?

(a) ^1⁄67

(b) ^1⁄24

(c) –^1⁄6

(d) –^1⁄12

This question was addressed to me by my college professor while I was bunking the class.

The query is from Application of Double Integrals in chapter Multiple Integrals of Engineering Mathematics

Answer 1

Right answer is (b) ^1⁄24

Explanation: \(\int_0^1 \int_{-√y}^{-y^2} y.x dxdy=\frac{1}{2} \int_0^1 y[y^4-y]dy=\frac{1}{2} [\frac{1}{6}-\frac{1}{3}]=-\frac{1}{12}\)