Would someone help me review my integration homework? Area between graphs is its focus.

Question

Would someone help me review my integration homework?  Area between graphs is its focus.

abdullah1995 · Answer

i can try.

anonymous · Answer

attachment

irishboy123 · Answer

looks good

zehanz · Answer

I guess you don't need any help :).
All your answers are correct.
I understand every step you wrote down.

One (tiny) point of criticism: in problem 3, the answer can be simplified just a little bit more to $\sqrt 2 -1$.

anonymous · Answer

@ZeHanz wolfram says that number 5 is incorrect, and it says it's 44/15, not 74/15, but I can't find the error

amistre64 · Answer

what are your permissible means of finding th eintersection points?

anonymous · Answer

seemingly any, including process of elimination

zehanz · Answer

It is just an silly error in one of the last steps: -96-40=-136, so the answer becomes (180-136)/15=44/15..

anonymous · Answer

doh, thanks for checking, good to go, and thanks to all for help

zehanz · Answer

YW!

amistre64 · Answer

just to work some algebra ....

x^4 -2x^3 +x^2 -x = x

x=0 is obvious, divide by x

x^3 -2x^2 +x -1 = 1

x^3 -2x^2 +x -2 = 0

factor

x^2(x -2) +x -2 = 0

factor again 

(x^2+x) (x -2) = 0

since x not = 0 so we could divide ...  x=2 is valid