Question

Integrate (2x-1)/(3)
I'm not so sure how to do this so any help would be appreciated. Thanks

Answer 1

\[\Large \int\limits \frac{2x-1}{3}dx\]So that's our integral? :)

Answer 2

Yes

Answer 3

I'm not so sure how to rearrange it into a simpler form for integrating

Answer 4

Using the definition of the integral?

Answer 5

Or using integral properties?

Answer 6

Well this is part of a question to find the area of a shaded segment

Answer 7

Well do you know how to do this: \[
\int x \;dx
\]?

Answer 8

= x^2/2

Answer 9

Okay. Well \[
\int \frac{2x+1}{3}dx = \frac{1}{3}\left( \int2x\;dx+\int dx\right)
\]

Answer 10

Does it equal to 1/3x^2
?

Answer 11

you're missing a term.

Answer 12

Well what is \[\int\limits dx\]? I'm not so sure because we never learnt it...

Answer 13

\[
\int dx=x+C
\]

Answer 14

So the answer is
\[\frac{ 1 }{ 3 }x^{2}\]
?

Answer 15

If \(f(x)dx= dx\) then what is \(f(x)\)?

Answer 16

1?

Answer 17

Oops make that 1/3x^2 + x

Answer 18

+C

Answer 19

Ok thanks so much!