Help me with Riemann sum approximation?

Question

The expression (1/20)(sqrt(1/20)+sqrt(2/20)+sqrt(3/20)+...+sqrt(20/20)) is a Riemann sum approximation for 

 

a) ∫ sqrt(x/20) dx from 0 to 1

 

b) ∫ sqrt(x) dx from 0 to 1

 

c) (1/20) ∫ sqrt(x/20) dx from 0 to 1

 

d) (1/20) ∫ sqrt(x) dx from 0 to 1

 

e) (1/20) ∫ sqrt(x) dx from 0 to 20

 

Please show all your work. 

Answer 1

There are 20 subdivided rectangulars from 0 to 1 under f(x) =sqrt(x),

   the base of each rectangular = 1/20

   the height of each rectangular is the sqrt of nth subdivision, which is right side of rectangular

The total area is  (1/20)(sqrt(1/20)) + (1/20)(sqrt(2/20)) + (1/20)(sqrt(3/20)) +...+ (1/20)(sqrt(20/20))

                                 =(1/20)(sqrt(1/20) + sqrt (2/20) + .....+ sqrt(20/20)     Ans. b)