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Areas and Definite Integrals
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Objectives Students will be able to Calculate a definite integral. Calculate the area between a curve and the x-axis over a given interval. Use definite integrals to application problems.
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Fundamental Theorem of Calculus For a continuous function f(x) over an interval [a, b], let F be any antiderivative of f. Then
![Fundamental Theorem of Calculus For a continuous function f(x) over an interval [a, b], let F be any antiderivative of f.](http://images.slideplayer.com/16/5180258/slides/slide_3.jpg "Then.")
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Example 1 Evaluate the definite integral
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Example 2 Evaluate the definite integral
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Example 3 Evaluate the definite integral
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Example 4 Evaluate the definite integral
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Example 5 Evaluate the definite integral
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Example 6 Find the area between and the x-axis from x = 2 to x = 4.
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Example 7 The graph of f(x) below consists of two straight line segments and two quarter circles. Find the value of
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Example 8 An oil tanker is leaking oil at the rate of (in barrels per hour), where t is the time (in hours) after the tanker hits a hidden rock (when t = 0). a.Find the total number of barrels that the ship will leak on the first day. b.Find the total number of barrels that the ship will leak on the second day.
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