Find the area bounded by the curve (y = 2 x ) and the (x ) -axis from (x = 0 ) to (x = 2 ).

Given that, (y = 2 x,0 x 2 ) rgb 0,0.39215686274509803,0 (-15.16,-11.76) rectangle (15.16,7.2); plot( , 2*cos((( ))*180/pi) ); % (0,0)--(1.1,1); (-14.98,-1.63) node f ; (0.2,2.2) node A ; (0,0) node O ; (1.57,0.3) node B ; (3.14,-2.3) node C ; (4.71,0.3) node D ; (6.28,2.3) node E ; (6.28,0.2) node F ; % From the figure, we need to find the area of the region(OABCDEF) A = 0 2x | 2 x|dx = 4 0 2 (2 x) dx = 8( x) 0 2 = 8 sq. units

Application of Integrals — Class 12 Maths Solution

exemplar la LA NCERT Exemp. Ex. 1.3, Q. 22, Page 177

Question

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

Step-by-step Solution

Given that,
$y = 2\cos x,0 \le x \le 2\pi$

From the figure, we need to find the area of the region(OABCDEF)

$A = \int_0^{2x} | 2\cos x|dx$

$= 4\int_0^{\pi 2} {(2\cos x)} dx = 8(\sin x)_0^{\sqrt 2 } = 8$ sq. units

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