Area Under Curve

What statement best describes the Riemann Sum?

• 4 intervals, with heights using middle values

• 4 intervals, with heights using left values

• 5 intervals, with heights using middle values

• 5 intervals, with heights using right values

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

• 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

Sketch the function  $g\left(x\right)=4+\sqrt{x-3}$  . Then approximate  $A\left(g,\ 5\le x\le8\right)$  
 by both using six right endpoint rectangles and six left endpoint rectangles. Write both of the sums using sigma notation.

• Left endpoint:  $\frac{1}{2}\sum_{n=1}^6\left(4+\sqrt{\left(0.5n+5\right)-3}\right)\approx17.771$  
  
  Right endpoint: $\frac{1}{2}\sum_{n=0}^5\left(4+\sqrt{\left(0.5n+5\right)-3}\right)\approx17.360$  

• Left endpoint:  $\frac{1}{2}\sum_{n=0}^5\left(4+\sqrt{\left(0.5n\right)-3}\right)\approx17.360$  
  Right endpoint:  $\frac{1}{2}\sum_{n=1}^6\left(4+\sqrt{\left(0.5n\right)-3}\right)\approx17.771$  

• Left endpoint:  $\frac{1}{2}\sum_{n=0}^5\left(4+\sqrt{\left(0.5n+5\right)-3}\right)\approx17.360$ 
  
  Right endpoint:  $\frac{1}{2}\sum_{n=1}^6\left(4+\sqrt{\left(0.5n+5\right)-3}\right)\approx17.771$  

• Left endpoint:  $\frac{1}{2}\sum_{n=1}^6\left(4+\sqrt{\left(0.5n\right)-3}\right)\approx17.360$  
  Right endpoint:  $\frac{1}{2}\sum_{n=0}^5\left(4+\sqrt{\left(0.5n\right)-3}\right)\approx17.771$  

What is the value of the Riemann sum of h(x), using 4 subintervals and heights using right values?

• 12

• 14

• 16

• 18

Estimate the area of the region using two intervals and heights using right values. Then estimate the area using four intervals and heights using right values.

What is the difference between the two estimates?

• 0

• 2.5

• 5.75

• 8

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