Monday

July 28, 2014

July 28, 2014

Posted by **Robert** on Friday, September 7, 2012 at 9:44am.

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(1-25x^2)

dv = dx

v = x

so we get:

= 10 sin^-1 (5x)(x) - ∫50x/(1-25x^2)

= 10 sin^-1 (5x)(x)|1/5, 1/10 -

∫50x/(1-25x^2) |1/5, 1/10

let w = 1-25x^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!

- Calculus -
**Steve**, Friday, September 7, 2012 at 10:07amYou're ok to this point:

10 sin^-1 (5x)(x) + 2√(1-25x^2) + C |1/5, 1/10

By this time you should realize that radians are the measure of choice for trig stuff.

sin^-1(1/2) = pi/6

sin^-1(1) = pi/2

so you end up with

[10(1/5 * pi/2) + 2√(1-1)] - [10(1/10 * pi/6) + 2√(1-1/4)]

pi - (pi/6 + √3)

5pi/6 - √3

- Calculus -
**Reiny**, Friday, September 7, 2012 at 10:15amI think you dropped a square root and a dx in

**so we get:**

= 10 sin^-1 (5x)(x) - ∫50x/(1-25x^2)

I got

= 10 sin^-1 (5x)(x) - ∫50x/(1-25x^2)^(1/2) dx

that last part can be integrated as

-2(1 - 25x^2)^(1/2)

or -2√(1-25x^2)

so your final integral answer would be

10x sin^-1 (5x) - 2(1-25x^2)^(1/2)

see if that works for you.

- Calculus -
**Robert**, Friday, September 7, 2012 at 7:57pmTHanks Steve and Reiny!

**Related Questions**

Definite integral by parts (correction) - Hello, I just wanted to verify if my ...

Definite Integral - Calculate the following integral: upper limit: 1 lower limit...

math - How do you find the definite integral of an absolute function? ∫_0^...

integral calculus - Evaluate the following intergal:- integral of [Mvdv] with ...

12th Calculus - 1. Explain why the function f(x)=(x^2-4)/(x-2) is not continous ...

integral calculus.. - Evaluate the following integral:- Mvdv , with upper ...

integral calculus.. - Evaluate the following intergal:- Mvdv , with upper ...

calculus - Determine whether the following is convergent of divergent. integral(...

Calculus 2 - If n is a positive integer, prove that integral[(lnx)^ndx=((-1)^(n...

Calculus Fundamental Theorem - Evaluate the definite integral. function: x+13 ...