# Video: Evaluating the Definite Integral of a Function Containing Root Using Integration by Substitution

Convert the parametric equations π₯ = π‘Β² + 2 and π¦ = 3π‘ β 1 to rectangular form.

01:05

### Video Transcript

Convert the parametric equations π₯ equals π‘ squared plus two and π¦ equals three π‘ minus one to rectangular form.

Here, we have a pair of parametric equations. We have π₯ is equal to some function of π‘ and π¦ is equal to some other function of π‘. To convert parametric equations to rectangular form, we need to find a way to eliminate the π‘. So looking at our equations, we can see that we can rearrange the equation in π¦ to make π‘ the subject. We begin by adding one to both sides. And then, we divide through by three. So we see that π‘ is equal to π¦ plus one all over three.

Now, we go back to our equation for π₯. We replace π‘ with π¦ plus one over three. And we find that π₯ equals π¦ plus one over three all squared plus two. And there will be certain circumstances where weβre required to distribute the parentheses and simplify. In this case, thatβs not necessary. And so, weβre finished. Weβve converted the parametric equations π₯ equals π‘ squared plus two and π¦ equals three π‘ minus one into rectangular or Cartesian form. Itβs π₯ equals π¦ plus one over three all squared plus two.