Math Questions and Answers

Start Your Free Trial

The graph of a function f is shown.? Use the differential equation and the given point to find an equation of the function dy/dx = 4x+ (9x^2) / ( (3x^3 +1) ^3/2 )

Expert Answers info

Luca B. eNotes educator | Certified Educator

calendarEducator since 2011

write5,348 answers

starTop subjects are Math, Science, and Business

You need to find the function using the process of integration such that:

`int dy = int (4x+ (9x^2)/((3x^3 +1)^(3/2))) dx`

Using the property of linearity of integral yields:

`y = int 4x dx + int (9x^2)/((3x^3 +1)^(3/2))) dx`

`y = 4x^2/2 + int (9x^2)/((3x^3 +1)^(3/2))) dx`

You need to solve the integral `int (9x^2)/((3x^3 +1)^(3/2))) dx ` using the following substitution such that:

 `3x^3 + 1 = t => 9x^2...

(The entire section contains 192 words.)

Unlock This Answer Now

check Approved by eNotes Editorial