Evaluate the integral by reversing the order of integration?
Evaluate the integral by reversing the order of integration:
[ \int_{0}^{3} \int_{4}^{12} 8e^{x^2} \, dx \, dy ]
Thank you.
2 Answers
Feb 04, 2025
4 12
∫ ∫ 8e^x^2 dxdy
0 3y
=
12 x/3
∫ ∫ 8e^x^2 dydx
0 0
=
4/3 (from 0 to 12)∫ e^x^2 2x dx
u = x^2
du = 2x*dx
u_i = 0
u_f = 144
= 4/3 * (from 0 to 144)∫e^u du
= 4/3 * (e^144 - 1)
Hope this helps!
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