megannicole51
  • megannicole51
Find the integral of (x^6+4)^2 dx
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
square it!
anonymous
  • anonymous
\[\int(x^{12}+8x^6+16)dx\]
megannicole51
  • megannicole51
so....(x^6+4)(x^6+4)? and use foil to calculate?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
square, yeah
1 Attachment
megannicole51
  • megannicole51
hahah thats funny!
megannicole51
  • megannicole51
so is that the answer? i feel like it can't be that simple!
anonymous
  • anonymous
you made it to calculus right? time to drop "foil" from your vocab and no, that is not the answer, that is how you are going to find the answer right?
anonymous
  • anonymous
integrate term by term
dan815
  • dan815
the foil bomb
anonymous
  • anonymous
\[\int x^{12}dx+8\int x^6dx+\int 16dx\]
megannicole51
  • megannicole51
yeah im in calc 2 and at university....i like calling it foil.
anonymous
  • anonymous
use the power rule backwards for each \[\int x^ndx=\frac{x^{n+1}}{n+1}\]
anonymous
  • anonymous
you good from there?
dan815
  • dan815
do they start integration in calc 2?
megannicole51
  • megannicole51
yeah they do
megannicole51
  • megannicole51
my professor doesnt speak very good english so I'm trying to learn the material and try to understand what hes saying lol
megannicole51
  • megannicole51
and what do u mean the power rule backwards?
dan815
  • dan815
watch youtube videos on it there are a lot
dan815
  • dan815
derivative backwards
dan815
  • dan815
just think what do i need to take the derivative of to get that
dan815
  • dan815
like 16... d/dx of 16x = 16
dan815
  • dan815
d/dx of 16x+c is also=16
megannicole51
  • megannicole51
ooooh i get it but how would u do like x^10?
dan815
  • dan815
for x^6 .... d/dx of 1/7*x^7 = x^6
megannicole51
  • megannicole51
so it would be x^9?
anonymous
  • anonymous
\[\int x^{10}dx=\frac{x^{11}}{11}\] etc
dan815
  • dan815
d/dx 1/11 * x^11=x^10
anonymous
  • anonymous
add one to the exponent, then divide by that number
dan815
  • dan815
u addin +1 to exponent and dividing by thaat exponent
dan815
  • dan815
the inverse of derivative power formula
anonymous
  • anonymous
this is what i means by the power rule backwards \[\int x^ndx=\frac{x^{n+1}}{n+1}\] since the power rule is \[\frac{d}{dx}[x^n]=nx^{n-1}\]
dan815
  • dan815
for derivavtive u multiple my exp then subtract -1 from exp so backwards is +1 to exp and divide by exp
dan815
  • dan815
u multiply*
anonymous
  • anonymous
power rule multiply by the exponent, drop the power by 1 power rule backwards add one to the exponent, divide by it
dan815
  • dan815
loser!! buddy
dan815
  • dan815
hows java coming along
megannicole51
  • megannicole51
so if i had the integral of (x^12 dx+8) that would just be x^11?
dan815
  • dan815
no
megannicole51
  • megannicole51
okay im confused im sorry
dan815
  • dan815
ok ill make it simple
dan815
  • dan815
derivative of x^2 =?
megannicole51
  • megannicole51
2x
dan815
  • dan815
integral of 2x =?
megannicole51
  • megannicole51
2?
dan815
  • dan815
no its x^2
megannicole51
  • megannicole51
okay
dan815
  • dan815
try this
megannicole51
  • megannicole51
okay:)
dan815
  • dan815
3x^2
dan815
  • dan815
integral of that?
dan815
  • dan815
its gonna be confusing for the first week u will mix up derivatives and integrals, we all did, but u will get used to it
megannicole51
  • megannicole51
okay i dont understand how you are taking the integral simple equations....i dont remember how to do them
megannicole51
  • megannicole51
thanks for the reassurance :)
dan815
  • dan815
okAY look carefully what we are doing for derivative
megannicole51
  • megannicole51
yes i can take the derivative
dan815
  • dan815
d/dx of x^3 =
megannicole51
  • megannicole51
3x^2
megannicole51
  • megannicole51
so the integral is x^3?
anonymous
  • anonymous
\[\int xdx=\frac{x^2}{2}\\\int x^2dx=\frac{x^3}{3}\\\int x^3dx=\frac{x^4}{4}\\\int x^4dx=\frac{x^5}{5}\\\int x^ndx=\frac{x^{n+1}}{n+1}\]
dan815
  • dan815
yeah
dan815
  • dan815
break up the steps though, so for derivative u first multipled by the exponent and subtracted 1 from the exponent
megannicole51
  • megannicole51
so x^12 is x^13/13?
dan815
  • dan815
yes
megannicole51
  • megannicole51
ooooh okay
megannicole51
  • megannicole51
so what do u do if u just have say 5?
dan815
  • dan815
5x
dan815
  • dan815
theres a catch to all this though, there can be a constant there too
dan815
  • dan815
for example d/dx 5x+1 = 5 so is d/dx 5X +2 = 5 d/dx 5x+c = 5
dan815
  • dan815
so just keep doing whatever u are doing, but after u get ur integral answer just add a c to it
megannicole51
  • megannicole51
okay so for the actual problem it would be the integral of x^13/13+8x integral x^7/7 dx + integral 16x dx?
megannicole51
  • megannicole51
sorry i dont know how to make my equations look fancy lol
dan815
  • dan815
the integral and dx sighs are lost once u do the integration buy yes
megannicole51
  • megannicole51
so is that the answer to the problem? or is there more?
dan815
  • dan815
x^13/13+8x +x^7/7 +16x +c
dan815
  • dan815
that sthe answer
dan815
  • dan815
u can simplify it but ya
megannicole51
  • megannicole51
why is it set up like that? do u know?
dan815
  • dan815
like what
megannicole51
  • megannicole51
why do they take out the integrals?
dan815
  • dan815
its just an operator sign like d/dx
dan815
  • dan815
after u do d/dx of 5x
dan815
  • dan815
u will get 5 not d/dx of 5 right
megannicole51
  • megannicole51
my online thing says its wrong:(
dan815
  • dan815
samething with integral and dx d/dx mEANS DERIVATIVE WITH RESPECT TO X integral dx means integral with respect to x
megannicole51
  • megannicole51
so like change the 8x to 8? and 16x to 16?
dan815
  • dan815
what do u mean
megannicole51
  • megannicole51
the answer was wrong is there something we are missing?
dan815
  • dan815
did u add the c
megannicole51
  • megannicole51
yes
dan815
  • dan815
try without it then
megannicole51
  • megannicole51
nope didnt work
dan815
  • dan815
what are u entering
megannicole51
  • megannicole51
x^13/13+8x+x^7/7+16x+c
dan815
  • dan815
its 8x^7/7
dan815
  • dan815
why dont u add the 8x and 16x together too
megannicole51
  • megannicole51
then is it 16x^15/15?
dan815
  • dan815
wuuttt lool
dan815
  • dan815
where did that come from
megannicole51
  • megannicole51
because you took the 8x and made it 8x^7/7 and adding the 8x and 16x didnt work
dan815
  • dan815
no i made the x^7/7 8x^7/7
megannicole51
  • megannicole51
ooooooh lol
dan815
  • dan815
lol
megannicole51
  • megannicole51
nope that didnt work either
dan815
  • dan815
i remember these noob integration days... it seemed so confusing, i was looking at my teacher like some alien
megannicole51
  • megannicole51
exactly! lol i feel so lost and i have so much homework
dan815
  • dan815
dont woory in a week or 2 it will be 2nd nature
megannicole51
  • megannicole51
yeah i hope so....so what did we do wrong with this one:(
dan815
  • dan815
wait ill brb
megannicole51
  • megannicole51
is it in the beginning where we just distributed the 2 instead of using foil to solve the equation?
dan815
  • dan815
okay let me show you all the steps
dan815
  • dan815
(x^6+4)^2
dan815
  • dan815
|dw:1377741247034:dw|
megannicole51
  • megannicole51
lol i totally left the 8x in my answer hahaha im sorry i just didnt catch it
megannicole51
  • megannicole51
thank you so much for all of ur help.... :) wana help me with another one?:)
dan815
  • dan815
ok
dan815
  • dan815
just practice more u need to do lke atleast 50 more integration questions
dan815
  • dan815
i think ive integrated like 1000000 times since last year
dan815
  • dan815
definately more integration that derivatives
megannicole51
  • megannicole51
hahah yeah i need a lot more practice lol the integration of sin^3(8q) cos (8q) dq
dan815
  • dan815
|dw:1377742500209:dw|
megannicole51
  • megannicole51
is that 8*4 in the denominator?
dan815
  • dan815
yes
megannicole51
  • megannicole51
okay:) and then do the same for cos(8q)?
dan815
  • dan815
no ur done
dan815
  • dan815
u r
dan815
  • dan815
|dw:1377742649267:dw|
dan815
  • dan815
take its derivative
megannicole51
  • megannicole51
chain rule?
dan815
  • dan815
|dw:1377742693679:dw|
megannicole51
  • megannicole51
okay hold on brb
megannicole51
  • megannicole51
so it would be (32)(32sin8q*cos8q)-(sin^4(8q))/32^2
dan815
  • dan815
|dw:1377744098142:dw|
dan815
  • dan815
|dw:1377744110551:dw|
dan815
  • dan815
see it works
dan815
  • dan815
|dw:1377744217683:dw|
megannicole51
  • megannicole51
so is that the answer? why did i do the chain rule?

Looking for something else?

Not the answer you are looking for? Search for more explanations.