Question

integrate the definite integral from 1 to 5 of s/(s^2+4)^1/2

Answer 1

let s^2 + 4 =t
See if it helps.

Answer 2

so then we gt s/t^1/2

Answer 3

@forexpipz You will not get s/t^1/2

there is a ds also there
finally you should be getting t/t^1/2 or t^(-1/2) inside the integral.

Answer 4

Write down the integral in a proper way, to see what is going on:\[\int\limits_{1}^{5}\frac{ s }{ \sqrt{s^2+4} }ds\]Now set u = s² + 4, then du= 2s ds. Write the dividsion by a square root as a negative power (-1/2). Then you have:\[\frac{ 1 }{ 2 }\int\limits_{\sqrt{5}}^{\sqrt{29}}u^{-\frac{ 1 }{ 2 }}du\]Now the rest is easy...

Answer 5

Too hasty, I guess - the boundaries with u as variable are 5 and 29, so it's\[\frac{ 1 }{ 2 }\int\limits_{5}^{29}u^{-\frac{ 1 }{ 2 }}du\]