Question

What would be the way you'd anti derive 25∫cos(arctan(1.2/x)?

Answer 1

I dont need a solution just the method, ex: u sub

Answer 2

\[put ~arc \tan \frac{ 1.2 }{ x }=\theta \]
\[\frac{ 1.2 }{ x }=\tan \theta ,x=1.2 \cot \theta ,dx=-1.2\csc ^2 \theta~ d \theta \]
\[I=\int\limits \cos \theta (-1.2\csc ^2 \theta)d \theta=-1.2\int\limits \frac{ \cos \theta }{ \sin ^2 \theta }d \theta\]
\[=-1.2 \int\limits (\sin \theta)^{-2}\cos \theta d \theta=-1.2\frac{ \left( \sin \theta \right)^{-1} }{ -1 }+c\]
\[=\frac{ 1.2 }{ \sin \theta }+c\]
replace the value of theta

Answer 3

would this work if I had a definite integral that I was integrating over distance? Do I just use the derivative and plug in the values?

Answer 4

not the derivative sorry

Answer 5

if you are dealing with definite integral ,then find the new limits
and no need to come back to x

Answer 6

Oh thats super smart thanks.

Answer 7

uw