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Area enclosed by the curve y=f(x) define...

Area enclosed by the curve `y=f(x)` defined parametrically as `x=(1-t^2)/(1+t^2),y=(2t)/(1+t^2)i se q u a lto` `pis qdotu n i t s` (b) `pi/2s qdotu n i t s` `(3pi)/4s qdotu n i t s` (d) `(3pi)/2s qdotu n i t s`

A

`pi` sq. units

B

`pi//2` sq. units

C

`(3pi)/(4)` sq. units

D

`(3pi)/(2)` sq. units

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly t can be any real number
`"Let "t=tan theta rArr x=(1-tan^(2)theta)/(1+tan^(2)theta)`
`rArr" "x=cos 2theta and y =(2 tan theta)/(1+tan^(2)theta)=sin 2theta`
`rArr" "x^(2)+y^(2)=1`
Thus, required area is `pi` sq. units.
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CENGAGE-AREA-Exercise (Single)
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  4. The area bounded by the curve a^(2)y=x^(2)(x+a) and the x-axis is

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  5. The area between the curve y=2x^(4)-x^(2), the x-axis, and the ordinat...

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  6. The area of the closed figure bounded by x=-1x=2, and y={{:(-x^(2)+2",...

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  7. The value of the parameter a such that the area bounded by y=a^(2)x^(2...

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  8. The positive valu of the parameter 'k' for which the area of the figu...

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  9. The area bounded by the curve y=x(1-log(e)x) and x-axis is

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  10. The area inside the parabola 5x^(2)-y=0 but outside the parabola 2x^(2...

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  11. Area enclosed between the curves |y|=1-x^2a n dx^2+y^2=1 is (3pi-8)/3 ...

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  12. If A(n) is the area bounded by y=x and y=x^(n), n in N, then A(2).A(3)...

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  13. The area of the region is 1st quadrant bounded by the y-axis, y=(x)/(4...

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  14. The area of the closed figure bounded by y=(x^2)/2-2x+2 and the tangen...

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  15. The area of the region bounded by x^(2)+y^(2)-2x-3=0 and y=|x|+1 is

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  16. The area enclosed by the curve y=sqrt(4-x^2),ygeqsqrt(2)sin((xpi)/(2sq...

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  17. The area bounded by the curve y^(2)=1-x and the lines y=(|x|)/(x),x=-...

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  18. The area bounded by the curves y=(log)e xa n dy=((log)e x)^2 is e-2s q...

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