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BaoZhu
 one year ago
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
BaoZhu
 one year ago
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

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myininaya
 one year ago
Best ResponseYou've already chosen the best response.1May I ask what method of integration you chose?

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1you could have done this with just an algebraic substitution

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

BaoZhu
 one year ago
Best ResponseYou've already chosen the best response.0integral x^3*sqrt(16x^2)dx

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1expression* that follows that first equal sign

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

BaoZhu
 one year ago
Best ResponseYou've already chosen the best response.0i do not know where to start......

myininaya
 one year ago
Best 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.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1They 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

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

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

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

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1oh are those commas?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1ok what you wrote is good then

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1So use your equation not mine to approximate P(5.5)

BaoZhu
 one year ago
Best ResponseYou've already chosen the best response.0but how will it turn the equation into just 1 number?solve for x?

myininaya
 one year ago
Best 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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1there is only one variable

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1and you are asked to replace that variable x with 5.5

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1this will give you P(5.5)

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1and don't forget the 1/2 part on that one part

BaoZhu
 one year ago
Best ResponseYou've already chosen the best response.0but now i got it, 105625 would be the answer

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1no that isn't the answer

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1don't forget the half part on that last term

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1which you wrote earlier has 22500 which is fine

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1I'm talking about for that 1/2*45000 part you simplified it earlier to 22500
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