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  • Find the area bounded by the curve y = 2cos x and the x-axis from x = 0 to x = 2 \pi

Find the area bounded by the curve y = 2cos x and the x-axis from x = 0 to x = 2 \pi

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The curve given is y = 2cosx and x axis from x = 0 to x = 2  \pi

Below is the figure, 

Area of the region bounded by the curve  y=f(x) , the  x  -axis and the ordinates  x=a  and  x=b,  where  f(x)  is a continuous function defined on  [a, b],  is given by  A=\int_{a}^{b} f(x) d x or \int_{a}^{b} y d x

From the figure;

Required area  =\int_{0}^{2 \pi}|2 \cos x| \mathrm{d} \mathrm{x}=4 \int_{0}^{\frac{\pi}{2}}(2 \cos \mathrm{x}) \mathrm{dx}

\\=8[\sin \mathrm{x}]_{0}^{\frac{\pi}{2}}\\ =8 sq.units \\

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