Approximating Area

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

Based on the table, use a Right Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

Use 3 trapezoids to determine the approximate area of the shaded area.

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.

Approximate the area between the x-axis and f(x) = 2⁄x from x = 0.5 to x = 2

using a left Riemann sum with 3 equal subdivisions.

• 11/4 units²

• 11/3 units²

• 4 units²

• 3 units²

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.

Approximate the area between the x-axis and h(x) = 1/7-x from x = 2 to x = 5 using a left Riemann sum with 3 equal subdivisions.

• 37/60 units²

• 47/60 units²

• 75/81 units²

• 3/5 units²

How do we approximate the area of a plane region?

• By taking the limit of the summation of all n-rectangles as n approaches infinity.

• By taking the derivative of the function.

• By multiplying length and width.

• By using Chain Rule.

Approximate the area between the x-axis and h(x) = 1/7-x from x = 2 to x = 5 using a left Riemann sum with 3 equal subdivisions.

• 37/60 units²

• 47/60 units²

• 75/81 units²

• 3/5 units²