C4 Mixed Exercise 2E Question 7b

Hey Everyone,

I am stuck on question 7b from C3 Mixed Exercise 2E as the title says.
The question is this,

7. A curve has the parametric equations, x = t² - 1 , y = t - t³, where t is a parameter.
a. Draw the graph of the curve for -2 ≤ t ≤ 2
b. Find the area of the finite region enclosed by the loop.

So if you draw the graph you get this. So I know that the equation for the area would be: 4t² - 4t⁴ however if yo do this for the boundaries of 0 and -1 you just get 0. In the solutions they have used 1 and 0 as the boundaries, but I don't get why? Can someone please explain this?

Hey Everyone,

I am stuck on question 7b from C3 Mixed Exercise 2E as the title says.
The question is this,

7. A curve has the parametric equations, x = t² - 1 , y = t - t³, where t is a parameter.
a. Draw the graph of the curve for -2 ≤ t ≤ 2
b. Find the area of the finite region enclosed by the loop.

So if you draw the graph you get this. So I know that the equation for the area would be: 4t² - 4t⁴ however if yo do this for the boundaries of 0 and -1 you just get 0. In the solutions they have used 1 and 0 as the boundaries, but I don't get why? Can someone please explain this?

You need to use the limits of t, not x.

Use the equation x = t² - 1 to change your limits of 0 and -1 for x to the corresponding limits for t.