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
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!
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!