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Evaluate the following iterated integral if region of integration R is bounded by graphs of y = x² and y = 2x.
∫ ∫ (x³+4y)dydx
1. Sketch two graphs on the same x-y plane, we get the two intercepts points (0,0) and (2,4)
2. The boundary for the inside integral is from x^2 to 2x. Take the inside integral wrp to y, treat x as constant.
3. Subsitute the value of the boundary into the resulted expression to get the result
4. Take the outside integral of that result wrp to x with the boundary is from 0 to 2.
The answer for you to double check your work
1. The resulted expression after taking inside integral is 8x^2 - 2x^4
2. The final answer is 128/15
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