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# Double Integral : Horizontal and Vertical Simple Methods

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I have managed to evaluate the double integral using the horizontal simple method, and answer 63. But when I reverse the order (vertical simple method) I cannot reach the same answer of 63, I get 65.

1) Evaluate the double integral of f(x,y)=x+4y^2 over the triangular region with vertices (-2,2) (4,2) & (1,-1)

Check that reversing the order of integration gives the same answer?

https://brainmass.com/math/real-analysis/double-integral-horizontal-vertical-simple-methods-14042

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Please see the attached file for the complete solution.

We know that the equations of the given lines (sides) are y=-x, y=x+2 and y=2. Then if we ...

#### Solution Summary

A mystery is solved as to why two methods of integration give a supposedly different result.

\$2.49