#How to calculate a specific Integral

41 messages · Page 1 of 1 (latest)

cloud idolBOT
radiant peak
#

You can divide it into two cases

#

in order to get rid of the modulus

vagrant copperBOT
radiant peak
#

So check when sqrt(x+2)-x >= 0 and when sqrt(x+2)-x < 0

#

adjust the bounds

lament oak
#

yes exactly

#

then split the integral into 2 integrals (from 0 to 2 + from 2 to 4)

#

and from 0 to 2 will be + (module thing) while from 2 to 4 will be - (module thing)

lament oak
#

then you get the right xs and do the split thing

#

i mean look, when x is in [0; 2] the thing inside module is >=0 and when x is in [2; 4] the thing inside module is <= 0

#

so that's why we need to split this integral into two integrals (from 0 to 2 + from 2 to 4)

radiant peak
#

,w plot sqrt(x+2)-x between 0 and 4

vagrant copperBOT
lament oak
#

oh sorry yeah

#

edited the message

#

but i thing you got the idea

radiant peak
#

all |...| does is make the stuff below x-axis above, or turns negative into positive

#

so when sqrt(x+2) - x is negative you multiply it by -1 to make it positive

#

that's all

lament oak
#

here, look

#

i made a latex for you

#

how do i send it here @radiant peak

radiant peak
#

insert the code

lament oak
# 
\int_{0}^{4}\left| \sqrt{x+2} - x\right|dx = \int_{0}^{2} \sqrt{x+2} - xdx + \int_{2}^{4} -(\sqrt{x+2} - x)dx
vagrant copperBOT
# 
\[ \int_{0}^{4}\left| \sqrt{x+2} - x\right|dx = \int_{0}^{2} \sqrt{x+2} - xdx + \int_{2}^{4} -(\sqrt{x+2} - x) \: dx \]
587715738484211754.png
lament oak
#

here it is @near slate

radiant peak
#

also you can simply use \abs{}

lament oak
#

yes

radiant peak
#

,w Integrate[Abs[Sqrt[x+2]-x],{x,0,4}]

vagrant copperBOT
radiant peak
#

me too, show your work

#

damn

#

oh well you integrated wrong

#

(x+2)^(3/2) * 2/3 not 3/2

#

yes

#

but you divide by n+1 not multiply

#

and dividing by 3/2 is the same as multiplying by 2/3

#

what is F(0) here?

#

exactly