Thread: How do you find the area for these parametric equations?

1. How do you find the area for these parametric equations?

Find the area enclosed by the x-axis and the curve
x = 1 + e^t , y = t - t^2

The answer in the back of the book is: 3 - e

I literally have spent about 2 hours on this problem, and I feel like I almost have the idea of how to do it.

I set y = t - t^2 = 0 and came up with my values for t, which then gave me my x values for the boundary.

Thus, I then took the integral of the area between my obtained t values of 1 and 0 for the following equation:

(t-t^2)(e^t) dt

I eventually obtained the value of e - 1, wtf?

2. Originally Posted by Brandong954
Find the area enclosed by the x-axis and the curve
x = 1 + e^t , y = t - t^2

The answer in the back of the book is: 3 - e

I literally have spent about 2 hours on this problem, and I feel like I almost have the idea of how to do it.

I set y = t - t^2 = 0 and came up with my values for t, which then gave me my x values for the boundary.

Thus, I then took the integral of the area between my obtained t values of 1 and 0 for the following equation:

(t-t^2)(e^t) dt

I eventually obtained the value of e - 1, wtf?

3. $\int_0^1 (t-t^2)e^t dt=3-e$. Do the integration by parts.