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JEE Main 202125 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2021 · 25 February · Morning Shift · Mathematics · Area Under Curves

The graphs of sine and cosine functions, intersect each other at a...

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area AA. Then A4{A}^{4} is equal toThe graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points

Correct answer

0

Step-by-step solution

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points

A=∫π/45π/4(sin⁡x−cos⁡x)dxA = {∫}_{\pi / 4}^{5\pi / 4}\left(\sin x - \cos x\right)dx

=(−cos⁡x−sin⁡x)∣π/45π/4)</p><p>= \left(- \cos x - \sin x\right)\left|{}_{\pi / 4}^{5\pi / 4}\right)</p><p>= \left(- \left(\dfrac{- 1}{\sqrt{2}}\right) - \left(\dfrac{- 1}{\sqrt{2}}\right)\right) - \left(- \left(\dfrac{1}{\sqrt{2}}\right) - \left(\dfrac{1}{\sqrt{2}}\right)\right)</p><p></p><p>⇒ A = \dfrac{2}{\sqrt{2}} + \dfrac{2}{\sqrt{2}} = 2\sqrt{2}sq.units</p><p>sq. units</p><p>⇒ {A}^{4} = {\left(2\sqrt{2}\right)}^{4} = 16 \times 4 = 64

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