# Evaluate the definite integral \int_{-5}^1 \frac{1}{\sqrt{9-2x}} \, dx using appropriate...

## Question:

Evaluate the definite integral {eq}\int_{-5}^1 \frac{1}{\sqrt{9-2x}} \, dx {/eq} using appropriate substitution.

## Definite Integral:

We will use the substitution method to solve the integral where we will replace the part in the square root to t and then integrate with respect to variable t and then plug-in the bounds.

To solve the problem we will use the substitution method:

{eq}\int_{-5}^{1}\frac{dx}{\sqrt{9-2x}} {/eq}

Now let us put:

{eq}9-2x=t\\ -2dx=dt {/eq}

Now the integral becomes:

{eq}=\frac{-1}{2}\int t^{\frac{-1}{2}}dt\\ =-\sqrt{t}\\ =-\sqrt{9-2x} {/eq}

Now we will plug-in the bounds:

{eq}=\sqrt{19}-\sqrt{7} {/eq}