Find Anti Derivative of -5.4sin(3t) - Tips & Solutions

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SUMMARY

The anti-derivative of the function -5.4sin(3t) is 1.8cos(3t) + C. To solve this, one must factor out -5.4 from the integral and use the substitution u = 3t, leading to the integral of sin(u). The integration process requires careful attention to the differential, resulting in the final expression after substituting back for u.

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Homework Statement


What is the anti derivative of

-5.4sin(3t)

The Attempt at a Solution



I have not done this in a while and i can't seem to find my prev. notes but is it not

-5.4cos(3t)*3 + C
 
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Divide by the differential in the brackets...

and \frac{d}{dx}(cosX)=-sinX
 
Well, here are some little hints.

Take -5.4 out of the integral.

Let u = 3t du = 3dt.

So then you have (-5.4/3) Integral of sin(u)du.

Integrate and place the u with 3t once you are finished. (Note the integral of sin is NOT just cosin.)
 
ahhh right...so the correct answer should be

1.8cos3t

thanks
 

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