Home > Calculus > Determining the Length of a Curve

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

Answer 1

Ezra Adams

The arc length is #~~ 6.1356 #

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 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Aurora Alvarado

To find the length of an arc of the curve y = sqrt(x+2) from x = 1 to x = 7, you would use the arc length formula for a curve given by y = f(x):

Arc Length = ∫ [sqrt(1 + (f'(x))^2)] dx from x = a to x = b

First, find f'(x), then substitute it into the formula and integrate from x = 1 to x = 7.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.