Areas, Riemann Sums, and Definite Integrals (9.4.2)

Question 1

• As the number of rectangles used to approximate the area of a region increases, the approximation becomes more accurate. It is possible to find the exact area by letting the width of each rectangle approach zero, thus generating an infinite number of rectangles.

Answer 1

• As the number of rectangles used to approximate the area of a region increases, the approximation becomes more accurate. It is possible to find the exact area by letting the width of each rectangle approach zero, thus generating an infinite number of rectangles.

Question 2

• A function and the equation for the area between its graph and the x-axis are related by the antiderivative.

Answer 2

• A function and the equation for the area between its graph and the x-axis are related by the antiderivative.

Question 3

• The definite integral of f from a to b is the limit of the Riemann sum as the lengths of the subintervals approach zero.

Answer 3

• The definite integral of f from a to b is the limit of the Riemann sum as the lengths of the subintervals approach zero.