Question

Find the integration of \(\int\int0^x (x^2 + y^2) \,dxdy\), where x varies from 0 to 1.

(a) ^4⁄3

(b) ^5⁄3

(c) ^2⁄3

(d) 1

I got this question by my college professor while I was bunking the class.

I want to ask this question from Application of Double Integrals in chapter Multiple Integrals of Engineering Mathematics

Answer 1

Correct choice is (c) ^2⁄3

Best explanation: Add constant automatically

Given, f(x)=\(\int_0^1 \int_0^x (x^2+y^2) dydx = \int_0^1 (x^3+\frac{x^3}{3})dx=1+\frac{1}{3}=\frac{2}{3}\)