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Question

The area bounded by y=sin-1x,x=12 and x-axis is


A

12+1

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B

1-12

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C

π42

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D

π42+12-1

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Solution

The correct option is D

π42+12-1


Explanation for correct option

Finding the area of the region bounded by the curves

Given, y=sin-1x,x=12

Visualize the two equations on a graph.

We have to calculate the area of the shaded region OAB

The required area will be,=Area(OAB)=areaofrectangleOABC-areaofcurveOBCO=12×π4-0π/4sinydy=π42+cosy0π/4=π42+12-1

Hence, the correct answer is Option (D).


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