Integral of ( ( t ^ 2 )( cos( t ) ) ) dt =
Integral of u dv = u * v - integral of v du
where u = t ^ 2, dv = cos( t ) dt
du = 2t dt, v = sin( t )
( t ^ 2 )( sin( t ) ) - integral of ( ( sin( t ) )( 2t ) ) dt
Integral of ( ( sin( t ) )( 2t ) ) dt =
Integral of x dy = x * y - integral of y dx
where x = 2t, dy = sin( t ) dt
dx = 2, y = -cos( t )
( 2t )( -cos( t ) ) - integral of ( ( -cos( t ) )( 2 ) ) dt =
( -2t )( cos( t ) ) - ( 2 )( -sin( t ) ) =
( -2t )( cos( t ) ) + ( 2 )( sin( t ) ) =
Remember
( t ^ 2 )( sin( t ) ) - integral of ( ( sin( t ) )( 2t ) ) dt =
( t ^ 2 )( sin( t ) ) - ( ( -2t )( cos( t ) ) + ( 2 )( sin( t ) ) ) =
( t ^ 2 )( sin( t ) ) + ( 2t )( cos( t ) ) - ( 2 )( sin( t ) ) =
( ( t ^ 2 ) - 2 )( sin( t ) ) + ( 2t )( cos( t ) )
(t^2)cos(t)dt
Try using this.
Integral uv' = uv - integral u'v
u=t^2
u'=2*t
v=sin(t)
v'=cos(t)
So: integral (t^2)cos(t) = (t^2 * sin(t)) - integral (2*t*sin(t))
You will then have to integrate by parts the last integral (2*t*sin(t))
That will give you a start. Can't remember if that's really how you do it.
learn how to integrate by parts yourself!!! it's really straight forward...and if you can't do that, good luck with the harder stuff.....
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Integral of ( ( t ^ 2 )( cos( t ) ) ) dt =
Integral of u dv = u * v - integral of v du
where u = t ^ 2, dv = cos( t ) dt
du = 2t dt, v = sin( t )
Integral of ( ( t ^ 2 )( cos( t ) ) ) dt =
( t ^ 2 )( sin( t ) ) - integral of ( ( sin( t ) )( 2t ) ) dt
Integral of ( ( sin( t ) )( 2t ) ) dt =
Integral of x dy = x * y - integral of y dx
where x = 2t, dy = sin( t ) dt
dx = 2, y = -cos( t )
Integral of ( ( sin( t ) )( 2t ) ) dt =
( 2t )( -cos( t ) ) - integral of ( ( -cos( t ) )( 2 ) ) dt =
( -2t )( cos( t ) ) - ( 2 )( -sin( t ) ) =
( -2t )( cos( t ) ) + ( 2 )( sin( t ) ) =
Remember
Integral of ( ( t ^ 2 )( cos( t ) ) ) dt =
( t ^ 2 )( sin( t ) ) - integral of ( ( sin( t ) )( 2t ) ) dt =
( t ^ 2 )( sin( t ) ) - ( ( -2t )( cos( t ) ) + ( 2 )( sin( t ) ) ) =
( t ^ 2 )( sin( t ) ) + ( 2t )( cos( t ) ) - ( 2 )( sin( t ) ) =
( ( t ^ 2 ) - 2 )( sin( t ) ) + ( 2t )( cos( t ) )
(t^2)cos(t)dt
Try using this.
Integral uv' = uv - integral u'v
u=t^2
u'=2*t
v=sin(t)
v'=cos(t)
So: integral (t^2)cos(t) = (t^2 * sin(t)) - integral (2*t*sin(t))
You will then have to integrate by parts the last integral (2*t*sin(t))
That will give you a start. Can't remember if that's really how you do it.
learn how to integrate by parts yourself!!! it's really straight forward...and if you can't do that, good luck with the harder stuff.....