The area under the curve y = ∣ cos x − sin x ∣ , 0 ≤ x ≤ 2 π , and above x -axis is :

y = ∣ cos x − sin x ∣ Required area = 2 ∫ 0 π /4 ( cos x − sin x ) d x = 2 [ sin x + cos x 0 0 π /4 ] = 2 [ 2 2 − 1 ] = ( 2 2 − 2 ) sq. units

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesEasy2 minPYQ_2013

MathematicsEasysingle choice

The area under the curve $y = ∣ cos x - sin x ∣$ , $0 \leq x \leq \frac{π}{2}$ , and above $x$ -axis is :

Question diagram: The area under the curve y = ∣ cos x − sin x ∣ , 0 ≤ x ≤ 2 π

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Answer:

Solution:

$y = ∣ cos x - sin x ∣$
$Required area = 2 \int_{0}^{π /4} (cos x - sin x) d x = 2 [sin x + cos x 0_{0}^{π /4}] = 2 [\frac{2}{2} - 1] = (22 - 2) sq. units$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2013

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