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Question

The area of the smaller segment cut off from the circle x2+y2=9 by x=1 is


A

129sec-13-8squnits

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B

9sec-13-8squnits

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C

8-9sec-13squnits

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D

None of these

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Solution

The correct option is B

9sec-13-8squnits


Explanation for the correct option:

Finding the area of the smaller segment:

Given, equation of circle x2+y2=9

Area of the smaller part cuts by x=1

Plotting both the curves,

The equation of the circle is in blue curve while the equation of straight line is in green curve.

So, the right-sided portion of the circle cut by the straight line is the required area.

Thus, the required area is

=2139-x2dx(usingintegrationbyparts)=2×12x9-x2+9sin-11313(asweknow,a2-x2dx=xa2-x22+a22sin-1xa)=9×π2-8-9sin-113=9π2-sin-113-8=9cos-113-8=9sec-13-8sq.units

Hence, option (B) is the correct answer.


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