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Let f(x) = minimum (x+1, sqrt(1-x))" for...

Let `f(x)` = minimum `(x+1, sqrt(1-x))" for all "x le 1.` Then the area bounded by `y=f(x)` and the `x-"axis"` is

A

`(7)/(3)` sq. units

B

`(1)/(6)` sq. units

C

`(11)/(6)` sq. units

D

`(7)/(6)` sq. units

Text Solution

Verified by Experts

The correct Answer is:
D

Required area =Shaded region
`=overset(1)underset(0)int(x_(2)-x_(1))dy` (integrating along y-axis)
`=overset(1)underset(0)int[(1-y^(2))-(y-1)]dy`
`=(7)/(6)` sq. unit
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CENGAGE-AREA-Exercise (Single)
  1. Area enclosed by the curve y=f(x) defined parametrically as x=(1-t^(2)...

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  2. Let f(x) = minimum (x+1, sqrt(1-x))" for all "x le 1. Then the area bo...

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  3. The area of the closed figure bounded by x=-1, y=0, y=x^(2)+x+1, and t...

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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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  19. The area bounded by y = 3-|3-x| and y=6/(|x+1|) is

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  20. Find the area enclosed between the curves: y = loge (x + e) , x = loge...

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