Question

Would someone help check my integration homework please? Doc is attached. TIA

Answer 1

part 2 b is wrong

Answer 2

anything else you see awry?

Answer 3

not seeing exactly what is wrong with 2b...

Answer 4

You'll have to make a distinction between \[\Large \int\limits_{\color{red}1}^\color{green}3 f(x)dx\] and \[\Large \int\limits_\color{green}3^\color{red}1 f(x)dx\]

They are related, surely, but not the same.

:)

Answer 5

can someone explain to me how that answer is derived?

Answer 6

omg, it's freckles, my savior

Answer 7

Hey.
One sec while I process us your homework.

Answer 8

1 looks great

Answer 9

\[\int\limits_{1}^{3}f(x)dx=\int\limits_{0}^{3}f(x)dx-\int\limits_{0}^{1}f(x) dx\]
looks like you did the first one right since you are taking the area that is on 0 and 1 from the area that is on 0 and 3

Answer 10

the second one...
\[\int\limits_{a}^{b}f(x) dx=-\int\limits_{b}^{a}f(x) dx\]

if you switch the limits make sure your change the sign of the integral

Answer 11

so let's see you have
\[\int\limits_{3}^{1}f(x) dx=-\int\limits_{1}^{3}f(x) dx\]

Answer 12

but you already evaluated the integral next to the negative sign in the previous question

Answer 13

gotcha

Answer 14

so you see that a and b should be opposite values

Answer 15

also good on the last 2 questions of number 2

Answer 16

do you want to know why they are opposite values?

Answer 17

\[\int\limits_{a}^{b}f(x) dx=F(x)|_a^b=F(b)-F(a) \\ =-(F(a)-F(b))=-F(x)|_b^a=\int\limits_b^a -F(x) dx=- \int\limits_b^aF(x) dx\]

Answer 18

I see, processing that, and need to study up more on these rules

Answer 19

how do 3,4,5 look?

Answer 20

didn't see those

Answer 21

one sec

Answer 22

well on number 3
when you calculate the integral of 2x+1 on [-2,2]
you will get a net area

Answer 23

oh you subtracted but I see have a little problem with

Answer 24

I got how you got the heights of both triangles

Answer 25

how did you get the bases ?

Answer 26

yes, like that