Find the length of an arc y = sqrt(x+2) from x=1 to x = 7. Any help to answer this?

1 Answer
Apr 4, 2018

The arc length is #~~ 6.1356 #

Explanation:

The arc length is given by:

# L=int_(alpha)^(beta) \ sqrt(1+(dy/dx)^2) \ dx #

We have:

# y = sqrt(x+2) #

Differentiating wrt #x# we have:

# dy/dx = 1/(2sqrt(x+2)) #

So, the arc length is given by:

# L = int_1^7 \ sqrt(1+(1/(2sqrt(x+2)))^2) \ dx #

# \ \ = int_1^7 \ sqrt(1+1/(4(x+2))) \ dx #

# \ \ = int_1^7 \ sqrt((4(x+2)+1)/(4(x+2))) \ dx #

# \ \ = int_1^7 \ sqrt((4x+7)/(4x+8)) \ dx #

# \ \ ~~ 6.1356 #