I was wondering if someone could help me find the definite integral of this: int_(R1)^(R1) tdt/(t^2+k^2)^(3/2)

tramolatzqvg

tramolatzqvg

Answered question

2022-11-08

I was wondering if someone could help me find the definite integral of this:
R 1 R 2 t d t ( t 2 + K 2 ) 3 / 2

Answer & Explanation

Raven Hawkins

Raven Hawkins

Beginner2022-11-09Added 19 answers

Assuming K is constant...
x d x ( x 2 + k 2 ) 3 2
Let t = x 2 + k 2 , Then d t = 2 x d x or x d x = d t 2 Replace xdx and x 2 + k 2 in the equation with dt/2 and t respectively.
What you get is
t 3 2 d t 2
which when integrated gives 1 ( x 2 + k 2 ) 1 2
Put int the limits to get
1 ( R 1 2 + k 2 ) 1 2 1 ( R 2 2 + k 2 ) 1 2

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