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Numerade Educator

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Problem 37 Medium Difficulty

Find $ f $.

$ f'(t) = \sec t(\sec t + \tan t) $, $ \quad -\pi/2 \leqslant t \leqslant \pi/2 $, $ \quad f(\pi/4) = -1 $

Answer

$$=\tan t+\sec t-2-\sqrt{2}$$

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Video Transcript

for this problem. We're going to be taking the anti derivative. But then we actually have an initial condition so we can find the full anti derivative. So we're given the F prime of X. We'll use excellent set of tea. So the halftime of X is seeking ex or rather seeking second X. And he can act cuts can jacks. Okay. Mhm. So then based on this, we see that this is going to end up giving us when we take the um through this or when we multiply this through. That's going to be second squared X. You can spread X plus 2nd X. Tangent X. And the anti derivative of sequence squared X is going to be tangent X plus second tangent X. That's going to be just seeking exposed to connect and that's me plus please policy. But we know that when um X equals power before we get a negative one. So based on that, we know that C is going to be equal to uh negative two minus route to. So the final answer is going to be next to minus route to. This is gonna be our final answer for the anti derivative