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.
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.
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.
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.
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.