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

BaoZhu
 9 months 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
 9 months ago
Best ResponseYou've already chosen the best response.1you could have done this with just an algebraic substitution

myininaya
 9 months 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
 9 months ago
Best ResponseYou've already chosen the best response.0integral x^3*sqrt(16x^2)dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

myininaya
 9 months 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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