1. Jim Wang Mr. Brose Period 6
Riemann Sums
Jim Wang
Mr. Brose
Period 6

2. Approximate the Area under y = x² on [ 0,4 ]
4 rectangles whose height is given using the left endpoint
4 rectangles whose height is given using the right endpoint
4 rectangles whose height is given using the midpoint
4 trapezoids
Evaluate the integral directly

3. a) 4 rectangles whose height is given using the left endpoint
Left: ( b • h )
(1)0 + (1)1 + (1)4 + (1)9
Ans. = 14

4. b) 4 rectangles whose height is given using the right endpoint
Right: ( b • h )
(1)1 + (1)4 + (1)9 + (1)16
Ans. = 30

5. c) 4 rectangles whose height is given using the midpoint
Midpoint: ( b • h)
(1)1/4 + (1)9/4 + (1)25/4 + (1)49/4
Ans. = 84/4 or 21

6. d) 4 trapezoids Area of Trapezoid: ½ h ( b1 + b2 ) 1 2 3 4 ½ [ 44 ]
½ (1) [ ]
½ [ 44 ]
Ans. = 22

7. e) Evaluate the integral directly
Insert in Calculator:
f(x) = 04 x² dx
Ans. = 64/3