what is the integral of cos(log[x])dxwhere [.] denotes greatest integer function(i.e step value)
kaushik bhargav , 10 Years ago
Grade 12
6 grade maths> what is the integral of cos(log[x])dx whe...
1 Answerskaushik bhargav
Last Activity: 10 Years ago
∫ cos ( log x ) dx
integrate by parts
u = cos (log x)
du = - sin(log x) dx/x
dv = dx
v = x
∫ cos ( log x ) dx = x cos(log x) + ∫ sin (log x) dx
again integrate by parts
u = sin(log x)
du = cos(log x ) dx/x
dv = dx
v = x
∫ cos ( log x ) dx = x cos(log x) + x sin (log x ) - ∫ cos (log x ) dx
= 2∫ cos ( log x ) dx = x cos(log x) + x sin (log x )
= ∫ cos ( log x ) dx = (1/2)x [ cos(log x) + sin (log x ) ] + C
integrate by parts
u = cos (log x)
du = - sin(log x) dx/x
dv = dx
v = x
∫ cos ( log x ) dx = x cos(log x) + ∫ sin (log x) dx
again integrate by parts
u = sin(log x)
du = cos(log x ) dx/x
dv = dx
v = x
∫ cos ( log x ) dx = x cos(log x) + x sin (log x ) - ∫ cos (log x ) dx
= 2∫ cos ( log x ) dx = x cos(log x) + x sin (log x )
= ∫ cos ( log x ) dx = (1/2)x [ cos(log x) + sin (log x ) ] + C
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