Approximating Area Under Curves

Use a right Riemann Sum to approximate the area of the shaded area.

• 12

• 9

• 10

• 5

• 1.5

• 1.1418

• 1.1

• 1.4914

• 35

• 40.625

• 32.1

• 41

• $32,000

• $31,662.50

• 3,166,250 cents

• 3,200,000 cents

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

What is the approximate area under the curve, using 4 intervals with heights using left values?

• 20

• 14

• 10

• 8

What is the approximate area under the parabola using 4 intervals with heights using right values?

• 6

• 10

• 11

• 20

Which estimate of the area is the smallest?

• 2 intervals with heights using right values

• 2 intervals with heights using left values

• 2 intervals with heights using middle values

• 4 intervals with heights using left values

Which estimate of the area is the largest?

• 4 intervals with heights using right values 14

• 2 intervals with heights using middle values 12

• 2 intervals with heights using right values 16

• 4 intervals with heights using left values 14

What is the approximate area of the region, using 4 subintervals and heights using left values?

• 7.5

• 7.75

• 10

• 11.5