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Numerade Educator

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Problem 18 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ g(v) = 2\cos v - \dfrac{3}{\sqrt{1 - v^2}} $

Answer

$2 \sin v-3 \arcsin v+C \quad$ or $\quad 2 \sin v+3 \arccos v+C$

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Video Transcript

This problem, we're looking to find the anti derivative of the given function. The function we have is gov because is equal to two coats envy minus three over the square root of one minus b squared. Yeah, this is going to be some trig identities with integral that we want to remember. So first of all, co sign of the the integral of or the anti derivative co sign is sign, so r g v is going to be equal to sine V. And then I remember that that is the same thing right here as the sign. So then in verse co sign. So what we're going to have is um or that's the inverse Science will have minus arc sign -3 Art sign of the and then we want to add the constant C. And that will give us our final answer.