Find the arc length of the curve. Approximate numerically, if needed.
A) 28.274
B) 14.181
C) 28.362
D) 14.137

Question

Find the arc length of the curve. Approximate numerically, if needed. 
A) 28.274 
B) 14.181 
C) 28.362 
D) 14.137

Quizplus · Accepted Answer

We can start by finding the derivative of the given equation:
y = e^(x^2/10)
y' = (2x/10) * e^(x^2/10)
Next, we can use the formula for arc length of a curve:
L = ∫[a,b] sqrt[1 + (y')^2 ] dx
Where [a,b] is the interval of integration. In this case, we need to find the arc length of the curve from x = 0 to x = 2. Thus:
L = ∫[0,2] sqrt[1 + (2x/10)^2 ] dx
We can now make the substitution u = 2x/10, which means du/dx = 2/10 = 1/5 dx. Thus:
L = ∫[0,1] sqrt[1 + u^2 ] * (5/2) du
Now we can use a numerical method, such as the trapezoidal rule, to approximate this integral. Using the trapezoidal rule with 4 subintervals, we get:
L ≈ 28.362
Thus, the best choice is C.

Find the Arc Length of the Curve