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Evaluate the integrals.$$\int_{1}^{32} x^{-6 / 5} d x$$

Calculus 1 / AB

Chapter 5

Integrals

Section 4

The Fundamental Theorem of Calculus

Integration

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University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

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In mathematics, precalculu…

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In mathematics, a function…

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Evaluate the integrals.

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09:18

we're gonna get a girl from 1 to 32. Have x the negative 6/5 d X. So when we do an anti derivative, we add one to our exponents. So I'll have X. So I'm adding 5/5. So that's why it gets the negative 1/5 and you divide your new exponents. Negative 1/5 when you evaluate that from 1 to 32 32 is kind of a suspicious number. I'll bring that make up here 32 to the negative one. Oh, come on. One fifth divided by negative 1/5. That's F A B minus F of a one to the negative, 1/5 over. Negative 1/5. That's that way. Um, remember that the fifth power or the 1/5 power is the same as doing like the fifth root. And so I can actually think of this as as asking me to do the fifth root of 32 to the negative one over negative 1/5 over here. It doesn't matter what the power is. For one, it's just one over negative 1/5. The fifth through 32 is two. So if two to the negative one in the over negative 1/5 minus. There's two negatives over years. We'll make that into a plus. And one divided by 1/5 is five. If you bring that down here, we actually just have Ah, two to the negative. One is 1/2 times, uh, negative 5/1 plus five. So we end up with negative five house plus five, which is positive five house.

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