Need help with Definite integral
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Need help with Definite integral

[From: ] [author: ] [Date: 11-04-27] [Hit: ]
The process is the same.I hope this helps!......
Hi. I need to know how to find the definite integral of these equations:
dx/(3-x)^4/5 from 2 to -13
and
(e^x-1)^4 e^x dx from 0 to 1

-
1. Let u = 3 - x. Then,

du/dx = -1
du = -dx
-du = dx

When x = -13...

u(-13) = 16
u(2) = 1

So this yields:

- ∫(u = 1,16) u^(-4/5) du

By power rule:

-u^(-4/5 + 1)/(-4/5 + 1) | 1,16
= -u^(1/5)/(1/5) | 1,16
= -5u^(1/5) | 1,16

Finally, by FTC:

-5(16)^(1/5) - (-5(1)^(1/5))
≈ -3.7055 [proved: http://www.wolframalpha.com/input/?i=int…

You try the last problem by yourself! Hint: Let u = e^(x) - 1. Then, du = e^(x) dx. The process is the same.

I hope this helps!
1
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