Integral from 0 to 1 of (x^2)(e^x^3)
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Integral from 0 to 1 of (x^2)(e^x^3)

[From: ] [author: ] [Date: 11-05-05] [Hit: ]
so its e^u.x^2 is replaced with du, but since there is a factor of 3 missing, you balance it out by bringing a 1/3 to the outside of the integral.integrate e^u, which is still e^u.......
you need u-substitution.
let u=x^3
therefore, du= 3x^2 dx.
replace the x^3 in e^x^3 with u, so its e^u.
x^2 is replaced with du, but since there is a factor of 3 missing, you balance it out by bringing a 1/3 to the outside of the integral.

1/3 * integral from 0 to 1 of (e^u)du
integrate e^u, which is still e^u. Plug back in u with x^3.

f(x) = 1/3(e^x^3) from 0 to 1. Let it be f(1)-f(0).

1/3(e^1 - e^0)
1/3(e-1), or (e-1)/3
1
keywords: from,to,Integral,of,Integral from 0 to 1 of (x^2)(e^x^3)
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