Asked by maga
evaluate the double integral
∫R∫ ye^x^3 dA
for the region R is bounded by x=y/2, x=1, and y=0
∫R∫ ye^x^3 dA
for the region R is bounded by x=y/2, x=1, and y=0
Answers
Answered by
Steve
Just plug and chug:
∫[0,1]∫[0,2x] ye^x^3 dy dx
=∫[0,1] (1/2 y^2 e^x^3)[0,2x] dx
=∫[0,1] (1/2 4x^2 e^x^3) dx
= ∫[0,1] 2x^2 e^x^3 dx
= ∫[0,1] 2/3 e^x^3 d(x^3)
= 2/3 e^x^3[0,1]
= 2/3(e^1 - e^0)
= 2/3(e-1)
∫[0,1]∫[0,2x] ye^x^3 dy dx
=∫[0,1] (1/2 y^2 e^x^3)[0,2x] dx
=∫[0,1] (1/2 4x^2 e^x^3) dx
= ∫[0,1] 2x^2 e^x^3 dx
= ∫[0,1] 2/3 e^x^3 d(x^3)
= 2/3 e^x^3[0,1]
= 2/3(e^1 - e^0)
= 2/3(e-1)
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