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

Required area = ∫ 0 π / 2 cos x - sin x d x = ∫ 0 π / 4 cos x - sin x d x + ∫ π / 4 π / 2 sin x - cos x d x = sin x + cos x 0 π / 4 + - cos x - sin x π / 4 π / 2 = 2 - 1 - 1 - 2 = 2 2 - 2

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minPYQ_2017

MathematicsMediumsingle choice

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

Options:

Answer:

Solution:

Required area $= \int_{0}^{π / 2} |\cos x - \sin x| d x$

$= \int_{0}^{π / 4} (\cos x - \sin x) d x + \int_{π / 4}^{π / 2} (\sin x - \cos x) d x$

$= {[\sin x + \cos x]}_{0}^{π / 4} + {[- \cos x - \sin x]}_{π / 4}^{π / 2}$

$= (\sqrt{2} - 1) - (1 - \sqrt{2}) = 2 \sqrt{2} - 2$

Stream:BITSATSubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: PYQ_2017

Doubts & Discussion

Loading discussions...