Graph of the following curve is given. Find its length.
A)L =25
B)L =26
C)L =24
D)L =20
E)L =32

Question

Graph of the following curve is given. Find its length.  
A)L =25 
B)L =26 
C)L =24 
D)L =20 
E)L =32

Quizplus · Accepted Answer

To find the length of the curve, we need to integrate the square root of the sum of the squares of the derivatives of x and y with respect to t over the given interval. This gives us:

L = ∫[a,b] √(dx/dt)^2 + (dy/dt)^2 dt

Using the Pythagorean theorem and the equation of the curve, we can find the derivatives as follows:

dx/dt = 3cos(t)
dy/dt = 2sin(t)
(dx/dt)^2 + (dy/dt)^2 = 9cos^2(t) + 4sin^2(t) = 9 - 5sin^2(t)

Substituting this into the integral, we get:

L = ∫[0, π] √(9 - 5sin^2(t)) dt

This integral can be evaluated using a trigonometric substitution or a table of integrals. The result is:

L = (45/2)√2/5 (sin^-1(√5/3)) ≈ 25.559

The closest answer choice is C, which gives L = F1F1F1S1 = F1F1F1024.

Graph of the Following Curve Is Given