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 The area of the region described by A= \left \{ \left ( x,y \right ):x^{2}+y^{2} \leq 1\: and\: y^{2}\leq 1-x\right \}is:

  • Option 1)

    \frac{\pi }{2}-\frac{2}{3}

  • Option 2)

    \frac{\pi }{2}+\frac{2}{3}

  • Option 3)

    \frac{\pi }{2}+\frac{4}{3}

  • Option 4)

    \frac{\pi }{2}-\frac{4}{3}

 

Answers (1)

best_answer

aS LEARNT IN CONCEPT

Area along y axis -

Let y_{1}= f_{1}(x)\, and \, y_{2}= f_{2}(x) be two curve, then area bounded by the curves and the lines

y = a and y = b is

A=\int_{a}^{b}\left ( x_{2}-x_{1} \right )dy

- wherein

 

 Area=\frac{\pi}{2} +2\int_{0}^{1}\sqrt{1-x} dx

Area=\frac{\pi}{2} -2\left [ \frac{2(1-x)^\frac{3}{2}}{3} \right ]^1_0

Area=\frac{\pi}{2} +\frac{2}{3}\times 2 = \frac{\pi }{2}+\frac{4}{3}


Option 1)

\frac{\pi }{2}-\frac{2}{3}

Incorrect

Option 2)

\frac{\pi }{2}+\frac{2}{3}

Incorrect

Option 3)

\frac{\pi }{2}+\frac{4}{3}

Correct

Option 4)

\frac{\pi }{2}-\frac{4}{3}

Incorrect

Posted by

prateek

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