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Numerade Educator

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Problem 8 Easy Difficulty

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

$ f(x) = x^{3.4} - 2x^{\sqrt{2-1}} $

Answer

$F(x)=\frac{x^{4.4}}{4.4}-\frac{2 x^{\sqrt{2}}}{\sqrt{2}}+c$

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Video Transcript

So we want to find the most general anti derivative have this function. The function is F of X equals Next to 3.4. Yeah. Plus minus two. X. Finance two. X to the square root of two. So now that we have this um we want this is actually dispirited too minus one, two minus one. So that's what we have as a result. So our F of X. The anti derivative. Yeah. Is going to be the anti directive each the individual terms. So X to the 3.4 we take used the power rule. That's going to give us X to the 4.4 over 4.4. And that's getting -2 times x. The power. So we're going to add one which is get rid of this negative one here. So if you need to the power of the square root of two Over the Square Root of two. And all we have to do is that our constancy. And as a result of this, if we take F prime of X and just choose a random constant C. Regardless of what the constant is. Our F prime of X. Craft is the same as the original F graph, so we've done this correctly.