Definite Integral Applications

What is the formula for calculating the arc length of a curve using the definite integral?

When finding the arc length of a curve, what does the definite integral represent?

$$f\left(x\right)=e^{\ 2\ x}$$  on  $$\left[-2,0\right]$$   Which of the following integrals represents the arc length?

$$f\left(x\right)=4\ x^{\frac{3}{2}}-1$$  on  $$\left[\frac{1}{12},\frac{2}{9}\right]$$  

Approximate Arc Length

$$s\approx L$$  (4 decimal places)

(a)  

$$f\left(x\right)=7\left(x+6\right)^{\frac{3}{2}}$$  on  $$\left[3,19\right]$$  

Approximate Arc Length

$$s\approx L$$   (3 decimal places)

(a)  

$$R\left(x\right)=\frac{1}{x^2}$$  on  $$\left[1,k\right]$$  

Which integral represents the arc length?

$$f\left(x\right)=x\ \ln x$$  on  $$\left[1,e\right]$$  

Which integral represents the arc length?

$$f\left(x\right)=\frac{1}{4}\ x^2-\frac{1}{2}\ \ln x$$  on  $$\left[1,2\right]$$  

Find the approximate arc length.

$$f\left(x\right)=e^{\ 2\ x}$$  on  $$\left[-2,0\right]$$   Which of the following integrals represents the arc length?

$$f\left(x\right)=-\ln\left(\cos x\right)$$  on  $$\left[0,\frac{\pi}{3}\right]$$  

Approximate Arc Length

$$s\approx L$$   (3 decimal places)

(a)