Question

Find the value of \(\int\int \,xydxdy\) over the area b punded by parabola x = 2a and x^2 = 4ay, is?

(a) ^a^4⁄4

(b) ^a^4⁄3

(c) ^a^5⁄3

(d) ^a^2⁄3

I had been asked this question in homework.

My enquiry is from Application of Double Integrals topic in chapter Multiple Integrals of Engineering Mathematics

Answer 1

Correct answer is (b) ^a^4⁄3

Explanation: \(\int_0^2a \int_0^{x^2/4a} x.y dxdy=\int_0^{2a} xdx \int_0^{x^2/4a} ydy=\int_0^{2a}\frac{xx^4}{32a^2}dx\)

=\(\frac{1}{32a^2} \int_0^{2a}x^5 dx=\frac{a^4}{3}\)