Area Between the Parametric Curves

[Tchao]

Homework Statement

Find the area between the parametric curve, x(t)=cos(t), y(t)=sin^2(t) and the x-axis

Homework Equations

- A = ∫ₐᵇ y(t) x'(t) dt

The Attempt at a Solution

=http://imgur.com/a/UA48d - My work shown in the link provided without the bounds, sorry for not rotating the image and the poor quality. I am not sure exactly how you will find the bounds for this problem. When I type x(t)=cos(t) and y(t)=sin^2(t) into my calculator, the curve intersects the x-axis at x = -1, 1. Would -1, 1 be the bounds for this problem or do we set both -1 and 1 equal to either cos(t) or sin^2(t), to solve for your bounds?

 

[ehild]

Homework Statement

Find the area between the parametric curve, x(t)=cos(t), y(t)=sin^2(t) and the x-axis

Homework Equations

- A = ∫ₐᵇ y(t) x'(t) dt

The Attempt at a Solution

=http://imgur.com/a/UA48d - My work shown in the link provided without the bounds, sorry for not rotating the image and the poor quality. I am not sure exactly how you will find the bounds for this problem. When I type x(t)=cos(t) and y(t)=sin^2(t) into my calculator, the curve intersects the x-axis at x = -1, 1. Would -1, 1 be the bounds for this problem or do we set both -1 and 1 equal to either cos(t) or sin^2(t), to solve for your bounds?

Why is a minus sign in front of A?
You integrate with respect to t. The bounds should be also t values. What is t when the curve crosses the x axis? Plot the curve on the x,y plane.