Question

evaluate the following definite integral

Answer 1

\[\int\limits_{0}^{1} (u + 2) (u-3) du\]

Answer 2

I am guessing I would distribute here

Answer 3

\[\int\limits_{0}^{1} u^2 - u -6 du\]

Answer 4

now find the anti derivative of that

Answer 5

you are correct. Keep going

Answer 6

\[\frac{ u^3 }{ 3 } - \frac{ u^2 }{ 2} - 6u \]

Answer 7

Now plug in '1' and '0' and subtract them?

Answer 8

yes

Answer 9

okay I did something wrong. I got \[\frac{ -19 }{ 3 }\]

Answer 10

incorrect

Answer 11

if

\[\Large g(u) = \frac{ u^3 }{ 3 } - \frac{ u^2 }{ 2} - 6u\]

then g(1) = ??

Answer 12

-37/6?

Answer 13

wait

Answer 14

let's start with this \[\frac{ 2 }{ 6 } - \frac{ 3 }{ 6 } = -\frac{ 1 }{ 6 }\]

Answer 15

you are doing good :)

Answer 16

then \[-\frac{ 1 }{ 6 } - \frac{ 36 }{ 6 }\]

Answer 17

so the first result is -37/6?

Answer 18

Correct. \[\Large g(1) = -\frac{ 37 }{ 6 }\]

Answer 19

now compute g(0)

Answer 20

then subtract

g(1) - g(0)

Answer 21

\[\frac{ -37 }{ 6 }\]

Answer 22

yeah it turns out that g(0) = 0

Answer 23

so,

\[\Large \int\limits_{0}^{1} (u + 2) (u-3) du = -\frac{37}{6}\]

Answer 24

awesome, thanks!

Answer 25

you're welcome