Calculate the iterated integral.

Question

please help me i don't get this one.

Answer 1

Integrate the inner integral first, keeping y constant

x = 0 to 1. integrate 1 + 4xy, giving x + 2x²y.

Evaluated from 0 to 1 gives : 1 + 2y - (0) = 1 + 2y

Integrate 1+2y from y=1 to y = 3

This gives y + y². Evaluated between limits is 3 + 3² - 1 - 1 = 10