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Help me with Riemann sum approximation?

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. 
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1 Answer

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)
 

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