Explanation Given: c ( t ) = ( a cos t , b sin t ) A = Area of the shaded region Calculation: As the area of the shaded region is equal to the sum of the area of right triangle, plus the remaining area of shaded region. Area of the right triangle is given by A = 1 2 x y A = 1 2 a b sin t cos t Now, remaining area of shaded region is A = ∫ t 0 y ( t ) x ′ ( t ) d t A = − ∫ 0 t b sin t ( − a sin t ) d t A = a b ∫ 0 t sin 2 t A = a b

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ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 11.1, Problem 108E

To determine

To prove:

t=(2ab)A where A is the area of shaded region and also its given that c(t)=(x,y).

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Chapter 11.1, Problem 107E

Chapter 11.1, Problem 109E

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Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 6PQ Ch. 11.1 - Prob. 7PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E

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To prove: t = ( 2 a b ) A where A is the area of shaded region and also its given that c ( t ) = ( x , y ) .

Solution Summary: The author calculates that the area of the shaded region is equal to the sum of a right triangle, plus the remaining area.

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To prove:

t=(2ab)A where A is the area of shaded region and also its given that c(t)=(x,y).

Want to see the full answer?

Chapter 11 Solutions

To prove: t = ( 2 a b ) A where A is the area of shaded region and also its given that c ( t ) = ( x , y ) .

Solution Summary: The author calculates that the area of the shaded region is equal to the sum of a right triangle, plus the remaining area.

Concept explainers

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To prove: t=(2ab)A where A is the area of shaded region and also its given that c(t)=(x,y).

Want to see the full answer?

Chapter 11 Solutions

To prove:

t=(2ab)A where A is the area of shaded region and also its given that c(t)=(x,y).