Question

1. Calculate the Riemann sum for f(x) = sqrt(x) on the interval [0, 10] using the partition {0,2,5,10} and c 1 =1 , c 2 =4 , and c 3 =9 .

Answer 1

Riemann Sum = 13

Explanation:

Step1 : Calculate the widths of the sub intervals

Δx₁=2−0=2

Δx₂=5−2=3

Δx₃=10−5=5

Step 2: Calculate the values at the sample points

f(1) =
`√(1)` = 1

f(2) =
`√(4)` = 2

f(3)=
`√(9)` = 1

Riemann Sum = Δx₁f(1) + Δx₂f(2) + Δx₃f(3) = 2*1 + 3*2 + 5*1 = 13