anonymous
  • anonymous
integral of xcos4x with explanation please?
Mathematics
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anonymous
  • anonymous
integral of xcos4x with explanation please?
Mathematics
schrodinger
  • schrodinger
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EarthCitizen
  • EarthCitizen
use substitution
myininaya
  • myininaya
\[\int\limits_{}^{}x \sin(4x) dx=x \cdot \frac{-1}{4} \cos(4x)-\int\limits_{}^{}\frac{-1}{4} \cos(4x) dx\]
myininaya
  • myininaya
integration by parts

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anonymous
  • anonymous
Is there any calculus problem that myin can't solve?
EarthCitizen
  • EarthCitizen
are u sure it's not 4x^2
EarthCitizen
  • EarthCitizen
myin, it's an indefinite integral
anonymous
  • anonymous
\[1/4*\sin 4x *x +1/16*\cos 4x \]
myininaya
  • myininaya
i know it is an indefinite integral integration by parts is the way to do this one the way i showed above
EarthCitizen
  • EarthCitizen
*thunder*
anonymous
  • anonymous
\[\int\limits_{}^{}x \sin 4xdx\]\[u = x, du = dx\]\[dv = sen(4x)dx\]\[v = (1/4)\cos (4x)\]\[\int\limits_{}^{}udv = uv - \int\limits_{}^{}vdu\]\[\int\limits_{}^{}x \sin 4xdx = x(1/4)\cos 4x - \int\limits_{}^{}(1/4)\cos(4x)dx\]= x(1/4)cos 4x - (1/4)(-(1/4)sen(4x)) =x(1/4)cos 4x + (1/16)sen(4x)

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