Calculate the approximation for the given function and interval.

Question

L4,

f(x) = √2-x

[0,2]

Answer 1

I assume that you want to approximate ∫_{(from 0 to 2)}√(2-x)dx by using a Riemann Sum with 4 equal subintervals and left endpoints.

Dividing the interval [0,2] into 4 equal intervals, each interval has length 1/2 and the left endpoints are 0, 1/2, 1, 3/2.

Let f(x) = √(2-x)

∫_{(from 0 to 2)} √(2-x)dx ≈ f(0)(1/2) + f(1/2)(1/2) + f(1)(1/2) + f(3/2)(1/2)

= (1/2)[√2 + √1.5 + √1 + √0.5} = 2.173