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Evaluate the integral by reversing the order of integration?
S denotes integral sign
S from 0 to 1 * S from 6y to 6 * e^(x^2)dxdy
2 Answers
- kbLv 78 years agoFavorite Answer
The region of integration (as written) is x = 6y to x = 6 with y in [0, 1].
After sketching this (do it!), we see that we can rewrite this as
y = 0 to y = x/6 with x in [0, 6].
So, the integral equals
∫(x = 0 to 6) ∫(y = 0 to x/6) 6e^(x^2) dy dx
= ∫(x = 0 to 6) 6ye^(x^2) {for y = 0 to x/6} dx
= ∫(x = 0 to 6) xe^(x^2) dx
= (1/2)e^(x^2) {for x = 0 to 6}
= (1/2)(e^36 - 1).
I hope this helps!
