For int_0^2 int_ sqrt x ^2 f(x, y) , dy , dx, what is the equivalent integral after changing order?

Home › MCQs › SSC Pure Mathematics › Question #4123

SSC Pure Mathematics QUESTION #4123

Question 1

For $\int_0^2 \int_{\sqrt{x}}^2 f(x, y) \, dy \, dx$, what is the equivalent integral after changing order?

$\int_0^2 \int_0^{y^2} f(x, y) \, dx \, dy$✔️
$\int_0^{\sqrt{2}} \int_0^{y^2} f(x, y) \, dx \, dy$
$\int_0^4 \int_0^{\sqrt{x}} f(x, y) \, dx \, dy$
$\int_{\sqrt{2}}^2 \int_0^{y^2} f(x, y) \, dx \, dy$

Correct Answer Explanation

Region: $0 \leq x \leq 2$ and $\sqrt{x} \leq y \leq 2$. This equals $0 \leq y \leq 2$ and $0 \leq x \leq y^2$. New integral: $\int_0^2 \int_0^{y^2} f(x, y) \, dx \, dy$.

More Options