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BaoZhu
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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
 8 months ago
 8 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
 8 months ago
 8 months ago

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myininaya Group TitleBest ResponseYou've already chosen the best response.1
May I ask what method of integration you chose?
 8 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.
 8 months ago

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

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

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

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
integral x^3*sqrt(16x^2)dx
 8 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
 8 months ago

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

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

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
one more question
 8 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?
 8 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
i do not know where to start......
 8 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.
 8 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
 8 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?
 8 months ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
We are given \[P(5)=45000; \text{ and } 120000 \cdot P'(5)=45000 ; \text{ and } 40000 \cdot P''(5)=45000\]
 8 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)
 8 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.
 8 months ago

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So use your equation not mine to approximate P(5.5)
 8 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?
 8 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
i don't understand
 8 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
 8 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
there is only one variable
 8 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
 8 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
this will give you P(5.5)
 8 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
 8 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
 8 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
 8 months ago

BaoZhu Group TitleBest ResponseYou've already chosen the best response.0
but now i got it, 105625 would be the answer
 8 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
 8 months ago

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
which you wrote earlier has 22500 which is fine
 8 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
 8 months ago
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