Question

I have a exam , help me please :<<

Answer 1

The value of double integration can be found by applying limits and integrating them one by one.

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

$\rm \int\limits \int\limits_R {ye^{-xy}} \, dA \ , R = [0,2]\times[0,3]$

After plugging limits:

$\rm \int\limits^3_0 \int\limits^2_0 {ye^{-xy}} \, dx dy$

After solving the first integration:

$\rm \int\limits^3_0 {(-e^{-2y}+1)} \, dy$

After solving the further integration and plugging limits:

$=\rm \dfrac{e^{-6}(5e^{6}+1)}{2}$

$\rm \int\limits \int\limits_R {ye^{-xy}} \, dA \ =\dfrac{e^{-6}(5e^{6}+1)}{2}$

Thus, the value of double integration can be found by applying limits and integrating them one by one.

Learn more about integration here:

brainly.com/question/18125359

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