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integration p/2 to -p/2 (sqrt(cosx-cos3x))
pi/2 to -pi/2 ∫ sqrt (cosx – cos 3x) dx= – [-pi/2 to pi/2 ∫ sqrt (cosx – cos 3x) dx]Since the function sqrt (cos x – cos 3x) is an even function, the difinite integral is equal to = – 2[ 0 to pi/2 ∫ sqrt (cosx – cos 3x) dx]= – 2[ 0 to pi/2 ∫ sqrt (2sin2x sinx) dx]= – 2 [ 0 to pi/2 ∫ sqrt (4 sin2x cosx) dx]= – 2 [ 0 to pi/2 ∫ 2 sinx sqrt(cosx) dx]= – 4[ 0 to pi/2 ∫ sinx sqrt(cosx) dx]Put cos x = t , – sin x dx = dt = 4 [ 1 to 0 ∫ sqrt(t) dt = – 4 [ 0 to 1 ∫ sqrt(t) dt = – 4 * 2/3 [t3/2] ( 0 to 1)= -8/3
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