Multiple choice

Changing the order of the integration in the double integral $I=\int\limits_0^8\int\limits^2_{\frac{x}{4}}f(x,y)dydx$ leads to $I=\int\limits_r^s\int\limits^q_pf(x,y)dydx$. What is the value of q?

  1. 4y

  2. 16y2

  3. x

  4. 8
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A Correct answer
Explanation

$\text{Given}\hspace{3cm}I=\int\limits_0^8\int\limits^2_{\pi/4}f(x,y)dydx \\ \text{Here we can draw the graoh from the limits of the integration, the limit of y is from$ y=\frac{x}{4}to$ y=2}\\ \text{For x the limit is$\hspace{1cm}$ x=0 to x=8} $

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