# Thread: unable to find my mistake with integration

1. ## unable to find my mistake with integration

find the arc length of 27y^2 = 4(x-2)^3 from ( 2,0) to (11, 6(3)^(1/2))?

by differentiation, i got dy/dx = 6 (27)^(1/2) (x-2)^(1/2)

and forming the integration equation i got,
integrate ( 972x - 1943) and

then finding the area form x=11 to x=2, my answer was 39375.

but the answer is supposed to be 14.

may i know where i gone wrong?

thanks!

2. Originally Posted by alexandrabel90
find the arc length of 27y^2 = 4(x-2)^3 from ( 2,0) to (11, 6(3)^(1/2))?

by differentiation, i got dy/dx = 6 (27)^(1/2) (x-2)^(1/2)
Apparently you differentiated incorrectly.

$\displaystyle y^2= \frac{4}{27}(x-2)^3$ so $\displaystyle y= \frac{2}{3\sqrt{3}}(x-2)^{3/2}$.

$\displaystyle \frac{dy}{dx}= \frac{(x- 2)^{1/2}}{\sqrt{3}}$.

From that $\displaystyle 1+ (dy/dx)^2= 1+ (x-2)^3/3$

and forming the integration equation i got,
integrate ( 972x - 1943) and

then finding the area form x=11 to x=2, my answer was 39375.

but the answer is supposed to be 14.

may i know where i gone wrong?

thanks!