Question

Help with integrals attached

Answer 1

you may have forgotten to attach

Answer 2

Sorry it wouldn't load

Answer 3

@Spacelimbus

Answer 4

I haven't heard of the limit process to be honest. However, within the definition of Riemann Integrability there can be limit term, for which you would just use the integration for the given expression. However I am not sure if that is what they mean.

Answer 5

Ok what would it look like? And i think it is talking about Reimann

Answer 6

just the integral of the function in that case \[\Large \int_{-1}^0 (x^2-x^3)dx \]

Answer 7

you gotta use a reimann sum, or can you just integrate using the fundamental theorem of calculus?

Answer 8

but I wouldn't take it for granted, as I said, haven't heard about limiting process before, it would make intuitive sense to me if they were talking about Riemann Sums and integration.

Answer 9

Ok so how would i right this and work it out in a Reimann Sum

Answer 10

this one would not be that bad actually since you can split it apart in two pieces
\[\int_{-1}^0x^2dx-\int_{-1}^0x^3dx\]

Answer 11

i can try to walk you through it if you like
it will take a bit of writing

Answer 12

ok sure!!!!! If its not too much trouble.

Answer 13

ok lets try the first one
\[\int_{-1}^0x^2dx\]
the interval is \([-1,0]\) and we divide up in to \(n\) equal parts
since the length of that interval is \(1\) each of them will have length \(\frac{1}{n}\) so you have

\[\Delta x=\frac{1}{n}\]

Answer 14

we can make \(x_0=-1, x_1=-1+\frac{1}{n}, x_2=-1+\frac{2}{n}, x_3=-1+\frac{3}{n}\) and in general we have
\[x_k=-1+\frac{k}{n}\]

Answer 15

now we need
\[\sum_{k=0}^nf(x_k)\Delta x=\sum_{k=0}^n\left(-1+\frac{k}{n}\right)^2\times \frac{1}{n}\]

Answer 16

told you this was going to take some time
you still with me here?

Answer 17

each step ok so far, or you have a question about any step? we have to do some basic algebra next

Answer 18

still there?

Answer 19

Sorry my computer timed out.