Integration Question

[kalyan601]

Hi, I've answered this question, but am not sure if it is correct or not:

The curve with equation y = f (x) passes through the point (1, 6). Given that
f'(x) = 3+ (5x² +2)/x^0.5 , x>0

find f (x) and simplify your answer to find the equation of the curve.

So here is what I did:

f'(x) = 3+ (5x²)/x^1/2 +(2)/x^1/2
= 3+5x^3/2 +2x^-1/2


So I integrated that to get:
3x + 2x^5/2 + 4x^1/2+ c

Substitute in x = 1 amd y = 6,

6=3 + 2+4+c
6=9+ c
c= - 3
So the equation is:

3x + 2x^5/2 + 4x^1/2 - 3

Is this correct?

Thanks

 

[HallsofIvy]

Except that if I were your teacher I would prefer that you write the answer as
y= 3x + 2x^(5/2) + 4x^(1/2) - 3, thus actually answering the question that was asked, that is fine.

 

[kalyan601]

Except that if I were your teacher I would prefer that you write the answer as
y= 3x + 2x^(5/2) + 4x^(1/2) - 3, thus actually answering the question that was asked, that is fine.

Thanks yeah, I added it in my answer now