Area Under Curve

  ∫₁³ 5x² dx

• a. 43

• b. 130/3

• c. 40

• d. 19/3

• 6

• 20

• 2

• 24

Find the area under the curve y =3x²-2x from x= 1 to x =5.

(Calculator allowed)

• 89

• 99

• 100

• 110

Approximate the area under the curve with a Riemann sum, using six sub-intervals and right endpoints.

• 8.25

• 8.374

• 8.35

• 8.30

Approximate the area under the curve with a Riemann Sum, using 4 sub-intervals and left endpoints.

• 1.67

• 1.60

• 1.55

• 1.66

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve.

• 5(3)+1(4)+2(5)+1(7)

• 5(3)+6(4)+8(5)+9(7)

• 5(4)+1(5)+2(7)+1(6)

• 0(3)+5(4)+6(5)+8(7)

Based on the table, use a trapezoidal sum of 4 sub-intervals to estimate the area under the curve.

(calculator allowed for arithmetic)

• 43

• 40.5

• 40

• 45

What does this picture represent?

• Left Riemann Sum

• Middle Riemann Sum

• Right Riemann Sum

• Trapezoidal Sum

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

Calculate the area for the shaded region on the parabola y = 8 - 2x - x²

• 63.64 units²

• 18.34 units²

• 4.56 units²

• 30.67 units²

• 39.33 units²