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JH
Numerade Educator

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Problem 2 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int_0^1 (3x + 1)^{\sqrt{2}}\ dx $

Answer

$\frac{4^{\sqrt{2}+1}-1}{3(\sqrt{2}+1)}$

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Video Transcript

Let's evaluate the given in several here, we should take you to be three x plus one. So this is using They use up, then do you? Over three. It's the X. So here we can rewrite this in overall. So watch out for these limits of integration. So plug in X equals zero We ate you equals one and then plugging in X equals one gives you eagles for so that's the upper bound. Then we know that we're supposed to have a one over three year from this from the use up, and then they're so here in parentheses. That's just you. And now we raise that to the swearing to power. So now, to do this in a girl, just use the power rule. So we add one to the exponents, and then we divide by the exponents and then plugging your end points and subtract. So again, four Route two plus one minus one all over this and that's your final answer.