Question

give explanation for following integral​

Answer 1

Answer:

The answer is $-\sqrt{k^2-y^2}+c$

Step-by-step explanation:

Let the given integral be I

 $\Rightarrow I=\displaystyle \int\dfrac{ydy}{\sqrt{k^2-y^2}}$

$\boxed{\text{Substitute } k^2-y^2=t^2 \Rightarrow 0-2ydy=2tdt \\ \Rightarrow ydy=-tdt}$

$\Rightarrow I=\displaystyle \int \dfrac{-tdt}{t}=-\int dt=-t+c$

                $=-\sqrt{k^2-y^2}+c$