Estimate the area under the graph of

Question

A) Estimate the area under the graph of f(x)=25-x^2 from x=0 to x=5 using 5 approximating rectangles and right endpoints.

 

Estimate:______

 

B) Repeat part (A) using left endpoints

 

Estimate:______

 

C) Repeat part (A) using midpoints

 

Estimate:______

Answer 1

Numerical Approximation

of the Integral of 25 - x^2 dx

Find 6 points to make 5 rectangles [Riemann Approx]

f(0)  f(1)  f(2)  f(3)  f(4)  f(5)

Delta x  =  1

A/  Add f(0) thru f(4) x 1

B/  Add f(1) thru f(5) x 1

C/  5 Rectangles => 5 Midpoints

     Find  f(1/2)  f(3/2) .........f(9/2)

     Add these for the Midpoint approximation