Definite integral by parts (correction)
posted by Robert .
Hello, I just wanted to verify if my work was good.
Calculate the following integral by parts:
∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^1 (5x)dx
so first I named the variables:
u = 10 sin^1 (5x)
du = 50 / sqr(125x^2)
dv = dx
v = x
so we get:
= 10 sin^1 (5x)(x)  ∫50x/(125x^2)
= 10 sin^1 (5x)(x)1/5, 1/10 
∫50x/(125x^2) 1/5, 1/10
let w = 125x^2
dw = 50xdx
= 10 sin^1 (5x)(x) + ∫ 1/sqr(w)dw
= 10 sin^1 (5x)(x) + 2sqr(w) + C 1/5, 1/10
= 180  (30 + 2sqr(0.75))
= 148.27
Thanks!
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