MAT 266 Lecture 33: calculus with parametric equations
MAT266 – Lecture #33 9.2 calculus with parametric equations
Area: if the curve is given by x=g(t) and y =h(t)
x=a
a=g(t)
t=c
x =b
b =g(t)
t=d
You have to change the limits for the area integral.
Where the Standard equation would have been
, when using
parametric equations you use:
Example 1: Find the area of one arch of a cycloid.
Solve for between this range gives you one arch.
Plug into equation and solve
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Integrate
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Combine terms
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Example: Find the area enclosed by and y axis
