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Computing area with parametrically repre...

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., `x=x(t), y=(t),` then the area of the figure is evaluated by one of the three formulas :
`S=-overset(beta)underset(alpha)inty(t)x'(t)dt,`
`S=overset(beta)underset(alpha)intx(t)y'(t)dt,`
`S=(1)/(2)overset(beta)underset(alpha)int(xy'-yx')dt,`
Where `alpha and beta` are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t.
The area of the loop described as
`x=(t)/(3)(6-t),y=(t^(2))/(8)(6-t)` is

A

`(27)/(5)`

B

`(24)/(5)`

C

`(27)/(6)`

D

`(21)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
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