Question

intergration problem

Answer 1

my firsr step is antderv right

Answer 2

i have an idea (although i totally suck at these)

Answer 3

it will be easier to integrate in terms of \(y\) not \(x\) so lets solve each of these for \(x\)

Answer 4

the first one is \(x=y+1\) and the second is \(x=\frac{y^2-6}{2}\)

Answer 5

we also need to find the limits of integration
did you find where they intersect?

Answer 6

oh and to answer your question, no, the first step is not to find the anti derivative, the first step is to find the thing you need to integrate, both the integrand and the limits of integration
THEN you can take the anti - derivative to compute the integral

Answer 7

how to do that

Answer 8

set them equal and solve

Answer 9

\[y=x-1,y^2=2x+6\] replace the \(y\) in the second equation by \(x-1\) and solve
\[(x-1)^2=2x+6\] turns out you get an easy quadratic equation to solve (it factor, get integer solutions )

Answer 10

that is if you want to do it by hand
it if was me, i would cut to the chase
http://www.wolframalpha.com/input/?i=%28x-1%29^2%3D2x%2B6

Answer 11

k so i get x^2-4x+8

Answer 12

you get \(x=-1\) or \(x=5\)
the points where they intersect are \((-1,-2)\) and \((5,4)\)

Answer 13

hmm no i think if you do it by hand you get
\[x^2-2x+1=2x+6\\
x^2-4x-5=0\]

Answer 14

o wow yea yea

Answer 15

factors as\[(x-5)(x+1)=0\\
x=-1,x=5\]

Answer 16

ok then

Answer 17

now this is a parabola that opens sideways
so it will be easier to integrate wrt y not x

Answer 18

here is a picture
http://www.wolframalpha.com/input/?i=+y%3Dx+-+1%2C+y^2%3D2x%2B6

Answer 19

so if you want to integrate wrt y, you need to write each of these as a function of \(y\) i.e solve each for \(x\)

Answer 20

first one is
\[x=y+1\] second is
\[x=\frac{y^2-6}{2}\]

Answer 21

so far so good?

Answer 22

okey

Answer 23

now if we turn it sideways we see the line is above the parabola
the limits of integration in terms of y means we use the y values
\[\int_{-2}^5y+1-(\frac{y^2-6}{2})dy\]

Answer 24

do some algebra first maybe, then compute that integral

Answer 25

i have to take the antiderv right

Answer 26

i would do the algebra first
then take anti derivatives

Answer 27

oh u mean simplify

Answer 28

oops
\[\int_{-2}^5\left(\frac{-y^2}{2}+y+4\right)dy\]

Answer 29

seems good :)

Answer 30

thanks !

Answer 31

now take the anto right

Answer 32

NOW take anti derivatives

Answer 33

yeah i know you are dying to do it, do it now

Answer 34

okey tge y2/2 is confusing

Answer 35

would it be y3/6?

Answer 36

no

Answer 37

yes! just don't forgot - sign

Answer 38

\[-\frac{y^2}{6}\] for the first term

Answer 39

ok as @xapproachesinfinity said "yes" only "no"

Answer 40

oh yea sorry

Answer 41

the rest should be routine
anti derivative is
\[-\frac{y^2}{6}+\frac{y^2}{2}+4y\]
plug in 5, plug in -2 and subtract
if you do it right, you will get 18i think

Answer 42

so i get 12.5 after simliy

Answer 43

damn typo \[-\frac{y^3}{6}+\frac{y^2}{2}+4y\]

Answer 44

i think ur right one my firends got 18 two

Answer 45

me, i like to know what the answer is before i begin
http://www.wolframalpha.com/input/?i=+area+between+the+curves+y%3Dx+-+1%2C+y^2%3D2x%2B6

Answer 46

ok so i have more intergral problems but just much eaiser i am just stuck since i am new to all this so could u help me more?

Answer 47

ok sure why not

Answer 48

if i can
i kind of suck at these though

Answer 49

ok give me 5 minutes i am finishing somthing

Answer 50

kk

Answer 51

lets see