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Evaluate the integral.

$ \displaystyle \int^{3}_{0} (1 + 6w^2 - 10w^4) \,dw $

$-429$

01:00

Frank L.

01:06

Amrita B.

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

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We are doing the integral from 0 to 3 of this function, one plus six W. To the second. Power minus 10 W. to the 4th power D. W. Just double check your the right equation. Is that all? Yeah, the wrong equation. You start working through it. That would be an issue. So the derivative of W would be one when you add one to your exponent, two becomes three and then you divide by your new excellent six divided by three. Gives me too. Same thing with adding one to the exponent. And then 10 divided by five. Gives me too. You can double check that this is right because the derivative of what's in blue needs to be the original problem From 0-3. Uh so make sure you plug in your upper bound to all of those values. So that would be three plus or three cubed is 27 Times two. and give me 54 minus. Uh W to the 5th. Power 81 BW 2 3 to the fourth would be That times another three, Maybe 243. And then I got double that like 684. Okay. Yeah. Um But I also encourage people, even though this is sort of obvious that when you plug in your lower bound you get a bunch of zeros later on, we're gonna come across a situation where when you plug in zero is like eat the zero power and things like that, you might actually get values. So I never tell my students to ignore the zero. But when you start adding three plus 50 for minus 4 86 you should get a correct answer of negative 429 and that is the correct answer.

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