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Find the area of f\left ( x \right )= \sin x+\cos x between x= \pi /2\: \: and\: \: \pi

  • Option 1)

    2\left ( \sqrt{2}-1 \right )

  • Option 2)

    2\sqrt2

  • Option 3)

    2

  • Option 4)

    2\left ( \sqrt{2}+1 \right )

 

Answers (1)

best_answer

As we learnt 

 

Working rule for finding area -

 

If curves lies on both sides of x - axes, add their moduli to get total area

- wherein

Area = |A_{1}|+|A_{2}|+|A_{3}|+|A_{4}|

 

 Area =\int_{\pi/2}^{3\pi/4}\left ( \sin x+\cos x \right )dx-\int_{3\pi/4}^{\pi}\left ( \sin x+\cos x \right )dx

              =\left [ \sin x-\cos x \right ]^{3\pi/4}_{\pi/2}-\left [ \sin x-\cos x \right ]^{\pi}_{3\pi/4}

              =\sqrt{2}-1-\left ( 1-\sqrt{2} \right )=2\sqrt{2}

 


Option 1)

2\left ( \sqrt{2}-1 \right )

Option 2)

2\sqrt2

Option 3)

2

Option 4)

2\left ( \sqrt{2}+1 \right )

Posted by

prateek

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