CasualCanadian

Determine if the improper integrals below are convergent or divergent. For a convergent integral calculate its value.

a. ∫ dx/cube√x from 2 to ∞

b. ∫ 3e^(1/2*x) dx from -∞ to 0

Please help me to understand by explaining the steps you followed to reach your answer.

Thanks in advance

Find the area between the curves y=2x^(2)+1 and y=13-2x

Where do I start? Can someone please explain how I would solve this using integration?

Thanks in advance.

Evaluate over the interval [5,0]

∫2x√(x+4) dx

Please show your work

Thanks

I am looking for an answer to this question, and it is not a simple investment calculation. This is supposed to be using indefinite integrals to come up with the answer. So here goes:

Money is flowing into an investment at a constant rate of R dollars per year. If interest is compounded continuously at 9% per annum, determine R so that the value of the investment after 10 years will be $27000.

So, all that I know is:

P(t)=Po*e^i*t

where P(10) = 27000,

i = .09

t = 10

based on this equation alone, I came up with an answer of $10977.38, but this is not all of the equation. Any help would be greatly appreciated.

Thanks

Money is flowing into an investment at a constant rate of R dollars per year. If interest is compounded continuously at 9% per annum, determine R so that the value of the investment after 10 years will be $27,000.

Any takers?

Thanks,

Here is the question:

A company has determined that its margina revenue from the sale of x units of its product is 4x-3/sqrtx.

Find the total revenue function, if the revenue from the sale of 16 units of its product is $588.

What I have is:

R'(x)= 4x-3/sqrtx

R(x)=∫R'(x)

What I came for an answer is:

R(x)=4*x^2/2-3lnx^(-1/2)+71.84

Do you get the same result? If not, where am I going wrong? Please explain.

Thanks,

Find the following indefinite integral:

∫x/1-x^2 dx

Please show your work and explain how it is done.

Thanks,

Here's a question for you:

Find the indefinite integrals:

∫x^2*e^-x dx

I don’t know what to do next. I understand that:

∫x^r dx = [x^(r+1)/r+1] + C,

provided that r ≠ -1, and

∫be^(ax) dx = b/a*e^(ax) + C

Is it possible to integrate by combining the two so that I first isolate ∫x^2, then isolate ∫e^-x? If not, could you please explain why? Also, if you could explain how it should be done, that would be great, too.

Thanks,

Ok,

I'm starting to figure out the integration thing with regular numbers, etc. but how do you integrate natural log equations?

This is what I have:

∫[ln(2x)]^2/2x dx

I know that

∫x^-1 dx= ∫1/x dx = dx/x = ln x + C, x>0 and

∫x^-1 dx= ln |x| +C, x<0

But how do I do it in reverse order? Can anyone help me?

Ok, here's what I've got:

Find the indefinite integral:

∫((t+2)^2)/cuberoot t dx

What I have so far is:

= ∫((t+2)(t+2))/(t^1/3) dx

= ∫(t^2+4t+4)/( t^1/3) dx

= [t^(2+1)/(2+1) + 2t^(1+1) + 4+C]/(t^(1/3))

= (t^3+2t^2+4+C)/t^(4/3)

Am I even close? Please provide me with some help!!

Thanks!

Hi,

I am trying to figure out integration, and I am thoroughly stumped. I understand that integration is just a different term for reverse differentiation, but that's about all I have been able to grasp at this point. Can anyone help with this problem? Please show how you got your answer so that I can try it with another problem or two.

∫8x-3/2*√x+3/x^2+2dx

Thanks in advance.

I think I almost have this one figured out. I am just trying to isolate Po from the equation.

How much money must you put into an investment today to yeld a lump sum of $50,000 in 25 years time, if interest is compounded continuously at an apr of 5.25%?

P(t)=Poe^(i*t)

where t=25 years, i=.0525, and P(25)=$50,000.

I have:

50,000=Poe^(.0525*25)

0=Poe^(1.3125)-50000

Now I'm stuck. Do I divide by Po to get it on the right side of the equation? Please help!!!

Thanks in advance.

A financial institution advertises that it will triple your money in 11 years. Assuming interest is compounded continuously, what is the annual interest rate?

What I have for a base equation is:

P=Poe^i*T

Your help is greatly appreciated. Thanks in advance

Two banks offer different investment opportunities. Bank A offers 8.75% compounded daily, and bank B offers 8.5% compounded continuously. Which is the better investment?Support your answer with appropriate details.

This is the answer I came up with:

Assume:

P=$1

t=1 year

compounded daily:

A=1(1+.0875/365)^365*1

A=$1.09

compounded continuously:

e=lim n=>infinity (1+(1/n))^n

therefore Bank a offers the better return on the investment in the long term, because as n gets larger without bound, A approaches e.

Am I even close? Appreciate your input.

A manufacturer estimates that the total cost of producing x units of its product is C(x)=4xe^(-x/6)+30 dollars.

a. Determine the marginal cost function

b. Find the maximum and minimum costs of production, if production varies between 3 and 12 units.

Good luck with this one!

See if you can figure this one out:

Given f(x)=5-e^(-2x),

Determine the equation of the tangent line to the graph of x when x=0.

Any takers?

Thanks in advance!

Given f(x)=5-e^(-2x),

Find all intercepts and equations of all asymptotes for the graph of f.

Find the derivative of g(t)=ln[ln(e^(1-t))] in simplified form.

Any takers?

Thanks

I have been struggling with this one.

A small business uses a minivan to make deliveries. The cost per hour of fuel for the van is C=v^2/600 dollars per hour, where v is the speed in miles per hour. If the driver is paid $6 per hour, find the speed of the van that minimizes the cost of a 100-mile trip. (Assume that there are no costs other than fuel and wages.)

Thanks in advance!!