Calculate volume

[neilvanas]

?(?) = 6/(x+a)
Area of f(x) from y-axis to x=b is 6ln3 units^2

When the area is rotated around the x-axis it gives a volume of 12π units^3

Determine the values of a and b

 

[nasi112]

area = [MATH]\int_{0}^{b} \ \frac{6}{x + a} \ dx = \ ?[/MATH]
volume [MATH]= \pi\int_0^b \left(\frac{6}{x + a}\right)^2 \ dx = \ ?[/MATH]
Solve those integrals. Compare the integral answers with the given answers, you will be able to make two equations that contains [MATH]a[/MATH] and [MATH]b[/MATH]. Then, by solving the two equations, you can find the the values of [MATH]a[/MATH] and [MATH]b[/MATH].

 

[neilvanas]

thank you, I will try it like that!

 

[neilvanas]

I did try, but I still can't find the answer, can you please explain a bit further?

 

[nasi112]

Let me see what you did. What is the answer you got for the integrals?

 

[neilvanas]

36π/a(a+b) and 6(ln(a+b)-ln(a))

 

[nasi112]

great

[MATH]6(\ln(a + b) - \ln(a)) = 6\ln(\frac{a + b}{a}) = 6\ln(3)[/MATH]
What does this tell you?

 

[neilvanas]

a+b/a = 3, so get b alone, then substitute into the volume formula

 

[nasi112]

a+b/a = 3, so get b alone, then substitute into the volume formula

Yes, correct.

So, what are the values of a and b?

 

[neilvanas]

a=2 and b=4?

 

[nasi112]

Yup those are the correct values. If you have any doubts, you can test them.

[MATH]\int_{0}^{4} \frac{6}{x + 2} \ dx = \ ?[/MATH]

 

[neilvanas]

Thank you very much for all the help, I really appreciate it!!

 

[nasi112]

You're welcome.