Question

Having trouble with basic integration please help. MEdals!

Answer 1

This is a property of integrals I believe.

Answer 2

So, you see that the limits of the very first integral go from -3 to 6. That's the domain we are integrating over.

Answer 3

I'll write it in a general form, and I hope you understand it. :3
\[\int\limits_{a}^{c} f(x) dx = \int\limits_{a}^{b} f(x) dx + \int\limits_{b}^{c} f(x) dx\]

Answer 4

I was trying to use this property but I thought I could just add a negative to the integral to flip the limits. Then i got confused :(

Answer 5

Nooo, that's added work and we don't need that.

Answer 6

So, we're given the value of two integrals within that domain, and we're solving the remaining one. For the first question.

Answer 7

I confused though, how am I supposed to take -3 to the bottom limit?

Answer 8

:o What are you talking about? Are we doing the first part? lol

Answer 9

-3 is less than 0. We're not doing anything fancy except using that property I showed ya.

Answer 10

The full integral goes from -6 to 3. We have integrals for -6 to -3 and 0 to 3. If we add up all those integrals within the full integrals, we can get the full integral.

10 = 12 + ? + 3

Answer 11

What we're trying to find is the integral that goes from -3 to 0.

Answer 12

ok so negative 5, I see..so i was looking at it the wrong way. I was viewing the integrals as separate problem..

Answer 13

Oh, I see. :o

Answer 14

I guess don't do that then lol.

Answer 15

For this second part, we'll have to use that property where you flip the limits and add the negative sign.
\[\int\limits_{3}^{-3} f(x) dx = -\int\limits_{-3}^{3} f(x) dx\]

Answer 16

2 for the second one

Answer 17

You got it. ;)

Answer 18

yeah its a conceptual error, i didn't fully realize how the integral notation fit together

Answer 19

thanks

Answer 20

No prob.