Riemann Sums

• 3

• 4

• 6

• 7

• left-endpoint rectanlges

• right-endpoint rectangles

• midpoint rectangles

• trapezoids

• the estimate will be too big

• the estimate will be too small

• the estimate will be exactly the same as the actual integral

• 0.25

• 0.5

• 1

• 3

• 0

• 0.5

• 1

• 1.5

• 0

• 1

• 1.5

• 4

• 3.5

• 4

• 5

• 6

• left-endpoint

• right endpoint

• midpoint

• trapezoids

• the estimate will be too big

• the estimate will be too small

• the estimate will be exactly the same as the actual integral