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Hello and welcome.
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We are looking at chapter 5, section 5, problem 37.
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So we're given some details, some information, and we're asked to find the following integral.
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So if you're not familiar, this notation means this is the second derivative of some function f.
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And if you notice we're given information about different values of f, different values of f prime as well.
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So if we want to taking the anti -derivative of this could be profitable.
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So that's kind of the approach we're going to take.
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So if i let u equal x, i know i can cancel that out pretty easily.
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So d -u equals d -x.
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And if d -v equals f double prime of x, d -x, then v is going to equal f -prime, just taking the anti -derivative of f double prime would be f prime of x so using integration by parts here that formula from one to four this would be u v minus the integral of v d u right so the that leads us to to the integral of f prime that's from 1 to 4 there is going to be f...