Question

Can you help me solve this please? http://screencast.com/t/ItHTxZTWBE

I know its simple. But if I see how you do it I will do much harder ones

Answer 1

there are a couple ways to do it

Answer 2

Can you tell me the one that goes somehow like f(x)-f(y) ??

Answer 3

ohh I didnt know about this graph

Answer 4

one way is to interpret the integral as the area under the "curve" \(y=0\) from \(x=0\) to \(x=3\)
geometry tells you it is the area of the above triangle, base is 3, height is 3, area is \(\frac{9}{2}\)

Answer 5

the other way is to find the "anti derivative" of \(x\) which is \(\frac{x^2}{2}\) then evaluate that at 3, and at 0, and subtract

Answer 6

i.e. say
\[F(x)=\frac{x^2}{2}\] so
\[\int_0^3xdx=F(3)-F(0)=\frac{3^2}{2}-\frac{0^2}{2}=\frac{9}{2}\]

Answer 7

i think you wanted the second way

Answer 8

I get it! Thanks a lot for the help! :)

Answer 9

yea!

Answer 10

yw