Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
BaoZhu
Group Title
integral x^3(sqrt(16x^2)dx
can someone check if my answer is right, (1024/3)((sqrt(16x^2)/(3)))^3+(1024/5)((sqrt(16x^2)/(3)))^5+C
 5 months ago
 5 months ago
BaoZhu Group Title
integral x^3(sqrt(16x^2)dx can someone check if my answer is right, (1024/3)((sqrt(16x^2)/(3)))^3+(1024/5)((sqrt(16x^2)/(3)))^5+C
 5 months ago
 5 months ago

This Question is Closed

myininaya Group TitleBest ResponseYou've already chosen the best response.1
May I ask what method of integration you chose?
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
first i used trig. sub. ax^2, gives x=4sintheta, and then i used trig. integral of usub.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you could have done this with just an algebraic substitution
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[u=16x^2 => du=2x dx \] \[x^2=16u \] So \[\int\limits_{}^{}x^2 \sqrt{16x^2} dx=\frac{1}{2}\int\limits_{}^{}x^2 \sqrt{16x^2} (2x) dx\] \[=\frac{1}{2}\int\limits_{}^{}(16u) \sqrt{u} du \] \[=\frac{1}{2}\int\limits_{}^{}(16 u^\frac{1}{2}u^\frac{3}{2}) du\]
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
but it's x^3, not x^2
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
integral x^3*sqrt(16x^2)dx
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I missed an x in that first part but and that next equation you see i have x^2 times x which is x^3
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
expression* that follows that first equal sign
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
do you see?
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
one more question
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Did you find P(x) as a 2nd degree taylor polynomial yet?
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
i do not know where to start......
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[P(x) \approx P(r)+P'(r)(xr)+\frac{1}{2}P''(r)(xr)^2 \] This is what they want you to use.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
They want you to use r as 5 and plug in the values they gave you for P'(5) and P''(5) Then they want you to find P(5.5) approximately using the resulting equation
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
so for 5, i got p5(x)=12000040000(x5)+22500(x5)^2, is this right so far?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[P(x)=45000+\frac{45000}{120000}(x5)+\frac{1}{2} \frac{45000}{40000}(x5)^2 \]
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
We are given \[P(5)=45000; \text{ and } 120000 \cdot P'(5)=45000 ; \text{ and } 40000 \cdot P''(5)=45000\]
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
That is how I got what was P'(5) and P''(5) and P(5)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
We will use that P I wrote to approximate the value of portfolio bonds when r is 5.5.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
oh are those commas?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I can't read.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
ok what you wrote is good then
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So use your equation not mine to approximate P(5.5)
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
but how will it turn the equation into just 1 number?solve for x?
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
i don't understand
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[P(x) \approx 12000040000(x5)+45000(x5)^2 \] You can find P(5.5) It will result in one number
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
there is only one variable
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
and you are asked to replace that variable x with 5.5
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
this will give you P(5.5)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
It is just like if i asked you to evaluate f(2) given f(x)=x5 you would say f(2)=25=3
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
oh thank you so much, i thought i have to replace 5.5 in as in term of r
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
and don't forget the 1/2 part on that one part
 5 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
but now i got it, 105625 would be the answer
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
yeah but you aren't given P''(5.5) or P'(5.5) or P(5.5) so that would be impossible
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
no that isn't the answer
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
don't forget the half part on that last term
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[P(x) \approx 12000040000(x5)+\frac{1}{2} 45000(x5)^2 \]
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
which you wrote earlier has 22500 which is fine
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I'm talking about for that 1/2*45000 part you simplified it earlier to 22500
 5 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.