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

In summary, the anti derivative of -5.4sin(3t) is 1.8cos(3t) plus a constant. To find the anti derivative, take -5.4 out of the integral and let u = 3t. Then, integrate and replace u with 3t in the final answer.
  • #1
unhip_crayon
34
0

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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  • #2
Divide by the differential in the brackets...

and [itex]\frac{d}{dx}(cosX)=-sinX[/itex]
 
  • #3
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.)
 
  • #4
ahhh right...so the correct answer should be

1.8cos3t

thanks
 

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

What is the formula for finding the anti-derivative of -5.4sin(3t)?

The general formula for finding the anti-derivative of a function is F(x) = ∫f(x)dx + C, where C is a constant. In this case, the anti-derivative of -5.4sin(3t) would be -5.4∫sin(3t)dt + C.

What is the power rule for finding the anti-derivative of a function?

The power rule for finding the anti-derivative of a function is F(x) = (1/n+1)f(x)^n+1 + C, where n is the power of the function. For example, if the function is x^2, the anti-derivative would be F(x) = (1/2+1)x^(2+1) + C = 1/3x^3 + C.

How do I handle coefficients when finding the anti-derivative?

When finding the anti-derivative, you can simply bring the coefficient outside of the integral and then apply the power rule. For example, if the function is 2x^3, the anti-derivative would be 2∫x^3dx = 2(1/3)x^4 + C = 2/3x^4 + C.

What is the constant of integration and why is it important?

The constant of integration, represented by C, is a constant added to the anti-derivative when finding the general solution. It is important because the derivative of a constant is always 0, so adding C allows for the possibility of multiple solutions to the anti-derivative.

Can I check my answer when finding the anti-derivative?

Yes, you can check your answer by taking the derivative of the anti-derivative you found. If the derivative is equal to the original function, then your answer is correct.

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