- anonymous

integral x^3(sqrt(16-x^2)dx
can someone check if my answer is right, (-1024/3)((sqrt(16-x^2)/(3)))^3+(1024/5)((sqrt(16-x^2)/(3)))^5+C

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- myininaya

May I ask what method of integration you chose?

- anonymous

first i used trig. sub. a-x^2, gives x=4sintheta, and then i used trig. integral of u-sub.

- myininaya

you could have done this with just an algebraic substitution

Looking for something else?

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

## More answers

- myininaya

\[u=16-x^2 => du=-2x dx \]
\[x^2=16-u \]
So \[\int\limits_{}^{}x^2 \sqrt{16-x^2} dx=\frac{-1}{2}\int\limits_{}^{}x^2 \sqrt{16-x^2} (-2x) dx\]
\[=\frac{-1}{2}\int\limits_{}^{}(16-u) \sqrt{u} du \]
\[=\frac{-1}{2}\int\limits_{}^{}(16 u^\frac{1}{2}-u^\frac{3}{2}) du\]

- anonymous

but it's x^3, not x^2

- anonymous

integral x^3*sqrt(16-x^2)dx

- myininaya

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

- myininaya

expression* that follows that first equal sign

- myininaya

do you see?

- anonymous

one more question

##### 1 Attachment

- myininaya

Did you find P(x) as a 2nd degree taylor polynomial yet?

- anonymous

i do not know where to start......

- myininaya

\[P(x) \approx P(r)+P'(r)(x-r)+\frac{1}{2}P''(r)(x-r)^2 \]
This is what they want you to use.

- myininaya

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

- anonymous

so for 5, i got p5(x)=120000-40000(x-5)+22500(x-5)^2, is this right so far?

- myininaya

\[P(x)=45000+\frac{45000}{120000}(x-5)+\frac{1}{2} \frac{45000}{-40000}(x-5)^2 \]

- myininaya

We are given \[P(5)=45000; \text{ and } 120000 \cdot P'(5)=45000 ; \text{ and } -40000 \cdot P''(5)=45000\]

- myininaya

That is how I got what was P'(5) and P''(5) and P(5)

- myininaya

We will use that P I wrote to approximate the value of portfolio bonds when r is 5.5.

- myininaya

oh are those commas?

- myininaya

lol

- myininaya

I can't read.

- myininaya

ok what you wrote is good then

- myininaya

So use your equation not mine to approximate P(5.5)

- anonymous

but how will it turn the equation into just 1 number?solve for x?

- anonymous

i don't understand

- myininaya

\[P(x) \approx 120000-40000(x-5)+45000(x-5)^2 \]
You can find P(5.5)
It will result in one number

- myininaya

there is only one variable

- myininaya

and you are asked to replace that variable x with 5.5

- myininaya

this will give you P(5.5)

- myininaya

It is just like if i asked you to evaluate f(2) given f(x)=x-5
you would say f(2)=2-5=-3

- anonymous

oh thank you so much, i thought i have to replace 5.5 in as in term of r

- myininaya

and don't forget the 1/2 part on that one part

- anonymous

but now i got it, 105625 would be the answer

- myininaya

yeah but you aren't given P''(5.5) or P'(5.5) or P(5.5) so that would be impossible

- myininaya

no that isn't the answer

- myininaya

don't forget the half part on that last term

- myininaya

\[P(x) \approx 120000-40000(x-5)+\frac{1}{2} 45000(x-5)^2 \]

- myininaya

which you wrote earlier has 22500 which is fine

- myininaya

I'm talking about for that 1/2*45000 part
you simplified it earlier to 22500

Looking for something else?

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