Reimann Sum approximation

Question

The expression 1/30 (sin 1/30 + sin 2/30 + sin 3/30.....+ sin 30/30) is a Reimann sum approximation for...

 

a) ∫sin (x/30) dx from 0 to 1

b) ∫sin x dx from 0 to 1

c) 1/30 ∫sin (x/30) dx from 0 to 1

d) 1/30 ∫sinx dx from 0 to 1

e) 1/30 ∫sinx dx from 0 to 30

Answer 1

Divide the interval [0,1] into 30 equal subintervals.

 

Using a right endpoint Riemann Sum with f(x) = sinx, we have:

 

   (1/30)sin(1/30) + (1/30)sin(2/30) + ... + (1/30)sin1 = ∫_{(from 0 to 1)}sinxdx

 

ANSWER:  b