Pls help me :((

[pls help me L((]

Find the perimeter of the loop of the curve 9?^2=?^2(2?+3)

 

[skeeter]

the loop is in the interval [MATH]-\frac{3}{2} \le x \le 0[/MATH]
using symmetry …

[MATH]S = 2 \int_{-\frac{3}{2}}^0 \sqrt{1+[f’(x)]^2} \, dx[/MATH]
where [MATH]f(x) = \dfrac{\sqrt{x^2(2x+3)}}{3}[/MATH]

 

[pls help me L((]

what would be my f′(x)?

 

[skeeter]

what would be my f′(x)?

[MATH]f(x) = \dfrac{1}{3}(2x^3+3x^2)^{\frac{1}{2}}[/MATH]
use the power rule & the chain rule to find [MATH]f'(x)[/MATH] ... you can do that on your own, correct?