- #1
James889
- 192
- 1
Hi,
Im trying to calculate the arc length of the function [tex]f(x)=x\sqrt{x}[/tex]
From x=1 to x=7
But I am getting the wrong answer and I am not sure why.
The formula is [tex]\int^{7}_{1}\sqrt{f'(x) + 1}[/tex]
The derivative of f(x) =[tex]\frac{x}{2\sqrt{x}} + \sqrt{x}[/tex]
Squaring yields [tex]~~\frac{x}{4} + 2x +1[/tex] which simplifies to:[tex]\frac{9x}{4}+1[/tex]
Integrating, we get [tex]\int\frac{2(\frac{9x^2}{2}+x)^{3/2}}{27}[/tex]
Inserting the limits of integration i get [tex]\frac{2*(9*49/2 +7)^{3/2}}{27} - \frac{2*(9/2 +1)^{3/2}}{27} = 253.222[/tex]
This is incorrect as the aswer should be something over 27.
What am i doing wrong?
Im trying to calculate the arc length of the function [tex]f(x)=x\sqrt{x}[/tex]
From x=1 to x=7
But I am getting the wrong answer and I am not sure why.
The formula is [tex]\int^{7}_{1}\sqrt{f'(x) + 1}[/tex]
The derivative of f(x) =[tex]\frac{x}{2\sqrt{x}} + \sqrt{x}[/tex]
Squaring yields [tex]~~\frac{x}{4} + 2x +1[/tex] which simplifies to:[tex]\frac{9x}{4}+1[/tex]
Integrating, we get [tex]\int\frac{2(\frac{9x^2}{2}+x)^{3/2}}{27}[/tex]
Inserting the limits of integration i get [tex]\frac{2*(9*49/2 +7)^{3/2}}{27} - \frac{2*(9/2 +1)^{3/2}}{27} = 253.222[/tex]
This is incorrect as the aswer should be something over 27.
What am i doing wrong?
Last edited: