Calculate the volume of the solid [question b]

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How to solve the below problem in question (b)?

a) Calculate the area of the region enclosed by the lines y = x, x = 0 and y + x = 2, and is above the plane xy.
b) Calculate the volume of the solid where it is enclosed from the region of (a) in the plane xy and the surface z = x^2 + y^2

Here is my solution:

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Please tell my if i solve it correct.

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Your first answer is correct.

If Im right, the second answer is $\frac{4}{3}$. You did all the calculus right, but you have a calculation mistake at the end.

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