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SSC Pure Mathematics QUESTION #4096
Question 1
After reversing the order of integration in \(\displaystyle\int_0^2\int_0^{\sqrt{x}}f(x,y)\,dy\,dx\), the correct equivalent integral is:
  • \(\displaystyle\int_0^2\int_0^{y^2}f(x,y)\,dx\,dy\)
  • \(\displaystyle\int_0^{\sqrt{2}}\int_{y^2}^{2}f(x,y)\,dx\,dy\)✔️
  • \(\displaystyle\int_0^{2}\int_{y}^{4}f(x,y)\,dx\,dy\)
  • \(\displaystyle\int_0^{1}\int_{y}^{2}f(x,y)\,dx\,dy\)
Correct Answer Explanation
Original region: \(0\leq x\leq2\), \(0\leq y\leq\sqrt{x}\), equivalently \(y^2\leq x\leq2\), \(0\leq y\leq\sqrt{2}\). Reversing order: integrate \(x\) from \(y^2\) to \(2\) first, then \(y\) from \(0\) to \(\sqrt{2}\).