Answer:
E(-9)≈3.4936
Step-by-step explanation:
Calculate the arc length of the following curve from x = 0 to x = π/2:
y(x) = -1 + 3 cos(x)
Hint: | The definition of arc length in Cartesian coordinates is s = integral_(x_0)^(x_1) sqrt(1 + y'(x)^2) dx.
Apply the definition of arc length to y(x) = -1 + 3 cos(x) for 0<x<π/2:
s = integral_0^(π/2) sqrt(1 + (d/dx(-1 + 3 cos(x)))^2) dx
Hint: | What is d/dx(-1 + 3 cos(x))?
Compute the derivative d/dx(-1 + 3 cos(x)):
= integral_0^(π/2) sqrt(1 + (-3 sin(x))^2) dx
Hint: | Can the integrand be simplified?
Simplify sqrt(1 + (-3 sin(x))^2):
= integral_0^(π/2) sqrt(1 + 9 sin^2(x)) dx
Hint: | Can this integral be computed?
Compute the definite integral:
Answer: E(-9)≈3.4936
