Illustrating the Fundamental Theorem of Calculus (9.4.5) Flashcards Preview

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Flashcards in Illustrating the Fundamental Theorem of Calculus (9.4.5) Deck (3)
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1
Q

• 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.

A

• 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.

2
Q

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

A

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

3
Q

• 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).

A

• 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).

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