Question

Integral Problem: I am unsure of what substitution method I should be using to solve this problem.

Answer 1

\[\int\limits_{.1}^{s} \frac{ ds }{ (s^{2}-0.01)^{1/2} }\]

Answer 2

well the answer would be before submitting the limits

Answer 3

sorry that should be 10s-1

Answer 4

\[-.\frac{ 250 }{ 10s-1 }+250\ln(10s+1)-\frac{ 250 }{ 10s+1 }-250\ln(10s-1)\]

Answer 5

Where do you get the 10 for "s"? and the "Ln(F(x))" What integration techniques did you use to solve for this?

Answer 6

Hey , use s^2 - 0.01 = t , you would get very easy form to be evaluated...

Answer 7

Nope, that won't work... If t=(s^(2)-0.01) Then du would be "2s ds" and the original equation does not contain an "s"

Answer 8

\[\Large \sec^2(x)-1=\tan^2(x) \]

Let
\[\Large u=0.1\sec\alpha \] then
\[\Large du=0.1\tan \alpha \sec \alpha d\alpha \]

Answer 9

Of course we need to match a few things, but this is what I try to get to:
\[\Large \int \frac{1}{0.1 \sqrt{\sec^2\alpha-1}} 0.1 \tan \alpha \sec \alpha d\alpha \]
If I didn't mess up any substitutions

Answer 10

There's a formula which says, Use that formula, and that's easy to prove...