Marlena B.

asked • 12/03/17

Calculate the derivative.

d/dx 0∫12x (cos^5 t)dt

1 Expert Answer

By:

Michael J. answered • 12/03/17

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Mastery of Limits, Derivatives, and Integration Techniques

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First find the integral of the cos5t.
 
∫cos5t dt =
 
∫(cost)(1 - sin2t)2 dt
 
 
Let        u = sint
           du = costdt
 
∫(1 - u2)2 du =
 
(1/3)(1 - u2)3 *(-1/2u) =
 
-(1/6u)(1 - u2)3 =
 
-(1/6u)(1 - sin2t)3
 
 
Now, find
 
d/dx[(-1/6sin12x)(1 - sin212x)3 + (1/6sin0)(1 - sin20)3]
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Michael J.

Correction:
 
∫(1 - u2)2 du =
 
∫(1 - 2u2 + u4) =
 
u - (2/3)u3 + (1/5)u5 =
 
sint - (2/3)sin3t + (1/5)sin5t
 
 
Then,
 
d/dx[sin(12x) - (2/3)sin3(12x) + (1/5)sin5(12x)]
 
Finish from there.
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12/03/17

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