Illustrating the Fundamental Theorem of Calculus (9.4.5)

Question 1

• The fundamental theorem of calculus enables you to evaluate definite integrals, thereby finding the area between the x-axis and a curve that lies above it. Area = integral(b a) f(x)dx.

Answer 1

• The fundamental theorem of calculus enables you to evaluate definite integrals, thereby finding the area between the x-axis and a curve that lies above it. Area = integral(b a) f(x)dx.

Question 2

• When the limits of integration are not given by the problem, find them by determining where the curve intersects the x-axis.

Answer 2

• When the limits of integration are not given by the problem, find them by determining where the curve intersects the x-axis.

Question 3

• The fundamental theorem of calculus states that if f is continuous on [a, b] and F is an antiderivative of f on that interal, then integral(b a) f(x)dx = F(b) - F(a).

Answer 3

• The fundamental theorem of calculus states that if f is continuous on [a, b] and F is an antiderivative of f on that interval, then integral(b a) f(x)dx = F(b) - F(a).