If a circle c with radius 1 rolls along the outside of the circle x2 + y2 = 36, a fixed point p on c traces out a curve called an epicycloid, with parametric equations x = 7 cos t − cos 7t, y = 7 sin t − sin 7t. find the area it encloses

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  area = 50π ≈ 157.08 square units

Step-by-step explanation:

The parameter t is the angle in the polar form equation of the curve. The square of the radius is the sum of squares of x and y. The area of a differential sector is ...

  dA = (1/2)r²·dt

The figure has 6-fold symmetry, so we only need to find the area of the first lobe of the curve. The integral is shown in the attachment, which evaluates it numerically.

The epicycloid encloses an area of 50π square units.

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