Question

Integral $\int_{0}^{2}\int_{y^{2}}^{y+2} dxdy$ equals

• A. $\int_{0}^{1}\int_{0}^{\sqrt{x}}dydx+\int_{1}^{2}\int_{x=2}^{\sqrt{x}}dy~dx$
• B. $\int_{0}^{2}\int_{0}^{\sqrt{x}}dydx+\int_{2}^{4}\int_{x=2}^{x}dydx$
• C. $\int_{0}^{2}\int_{0}^{\sqrt{x}}dydx+\int_{2}^{4}\int_{x-2}^{\sqrt{x}}dy~dx$
• D. $\int_{0}^{2}\int_{0}^{\sqrt{x}}dydx+\int_{2}^{4}\int_{0}^{4\sqrt{x}}dydx$

Hint:

To change the order of integration, always plot the boundaries. If any "lower" or "upper" boundary curve changes its formula halfway through the range, you must split the integral into multiple parts.

Answer 1

The Correct Option is C