Find the most general antiderivative of the function. Use C for any needed constant.
g(θ) = cos(θ) - 5sin(θ)
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what about
sinØ + 5cosØ + C
It is essential that you know these, if you are studying Calculus.
To find the most general antiderivative of the function g(θ) = cos(θ) - 5sin(θ), you can integrate term by term.
The antiderivative of cos(θ) is sin(θ), and the antiderivative of -5sin(θ) is -5cos(θ).
So, the antiderivative of g(θ) can be obtained by integrating each term separately:
∫ g(θ) dθ = ∫ (cos(θ) - 5sin(θ)) dθ
= ∫ cos(θ) dθ - ∫ 5sin(θ) dθ
= sin(θ) + (-5) ∫ sin(θ) dθ
Now, to find the antiderivative of sin(θ), we can use the trigonometric identity ∫ sin(θ) dθ = -cos(θ). Applying this, the equation becomes:
= sin(θ) - 5(-cos(θ))
= sin(θ) + 5cos(θ) + C
where C is the constant of integration, representing an arbitrary constant.
Therefore, the most general antiderivative of g(θ) = cos(θ) - 5sin(θ) is sin(θ) + 5cos(θ) + C.