Question

Help evaluating integrals given this information

Answer 1

Hint \[\LARGE \int\limits_a^b f(x) dx + \int\limits_b^c f(x)dx = \int\limits_a^c f(x)dx\]

Answer 2

Here's an example too \[\Large \int\limits_1^2 2xdx + \int\limits_2^3 2xdx = \int\limits_1^3 2xdx \] \[\Large x^2|_1^2 + x^2|_2^3 = x^2|_1^3 \\ \Large (2^2-1^2)+ (3^2-2^2) = 3^2-1^2\]

Answer 3

I am confused

Answer 4

I sort of understand the beginning part of that

Answer 5

Tell me more, what do you think?

Answer 6

I honestly do not know what to think, the integral from 8 -11 - the integral from 8 -9

Answer 7

I can't find an example of this even in my textbook

Answer 8

so if you have the integral from 8-11 and the integral from 8-9 then if you subtract them apart, you will have the integral from 9-11 now, does that make sense?

Answer 9

How do you know this @Kainui? Its like, you're the next Albert Einstein genius! I like that answer. (And sorry if I offended you). I don't mean to do it.

Answer 10

Hahaha I don't know how you could offend me by complimenting me. Thanks, I'm glad I could help!

Answer 11

okay, so if I wanted to find 9 to 10 I subtract 10-11 8-9?

Answer 12

yeah if you mean subtract both of those from that first one 8-11, yep!

Answer 13

but then I would get a negative

Answer 14

wait -13

Answer 15

thanks, I understand. now about tackling the second part.

Answer 16

-32

Answer 17

because the integral is -13 then you multiply it by 2 then subtract 6

Answer 18

correct?

Answer 19

Almost, except you have to separate it out, the -6 part is what's getting you. That's its own integral, just like if you were to take the derivative of this
\[2f(x)-6\] You would do each term individually right? You also have to integrate each term individually. The multiply by 2 part is correct though, good job. =)

Answer 20

got it thanks!