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Example 5 Video Example Evaluate the following integrals by interpreting each in terms of areas. f³√₂3 (b) √(x-3) dx (a) Solution √25-x² dx (a) Since f(x) = √25-x²20, we can interpret this integral as the area under the curve y = √25-x² from 0 to [ quarter-circle with radius in the figure below. Therefore, •f³√25 √25-x² dx = m(5)² = A₂ y=√√√25-x² or x² + y² = 25 (b) The graph of y = x - 3 is the line with slope y=x-3 5 3 A₁ (9,6) 9 X Q shown in the following figure. Ⓒ We compute the integral as the difference of the areas of the two triangles. √(x − 3) dx = A₁ - A₂ = -4.5=[ But, because y² = we get x² + y² = 25, which shows that the graph of f is the

Example 5 Video Example Evaluate the following integrals by interpreting each in terms of areas. f³√₂3 (b) √(x-3) dx (a) Solution √25-x² dx (a) Since f(x) = √25-x²20, we can interpret this integral as the area under the curve y = √25-x² from 0 to [ quarter-circle with radius in the figure below. Therefore, •f³√25 √25-x² dx = m(5)² = A₂ y=√√√25-x² or x² + y² = 25 (b) The graph of y = x - 3 is the line with slope y=x-3 5 3 A₁ (9,6) 9 X Q shown in the following figure. Ⓒ We compute the integral as the difference of the areas of the two triangles. √(x − 3) dx = A₁ - A₂ = -4.5=[ But, because y² = we get x² + y² = 25, which shows that the graph of f is the

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.CR: Chapter 7 Review
Problem 54CR
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Example 5 Video Example Evaluate the following integrals by interpreting each in terms of areas. (a) √25-x² dx (b) √(x-3) dx Solution (a) Since f(x) = √25-x²20, we can interpret this integral as the area under the curve y = √25-x² from 0 to [ quarter-circle with radius in the figure below. Therefore, •f³√25 √25-x² dx = m(5)² = A₂ y=√√√25-x² or x² + y² = 25 (b) The graph of y = x - 3 is the line with slope y=x-3 5 3 A₁ (9,6) 9 X Q shown in the following figure. Ⓒ We compute the integral as the difference of the areas of the two triangles. √(x − 3) dx = A₁ - A₂ = -4.5=[ But, because y² = we get x² + y² = 25, which shows that the graph of f is the
Transcribed Image Text:Example 5 Video Example Evaluate the following integrals by interpreting each in terms of areas. (a) √25-x² dx (b) √(x-3) dx Solution (a) Since f(x) = √25-x²20, we can interpret this integral as the area under the curve y = √25-x² from 0 to [ quarter-circle with radius in the figure below. Therefore, •f³√25 √25-x² dx = m(5)² = A₂ y=√√√25-x² or x² + y² = 25 (b) The graph of y = x - 3 is the line with slope y=x-3 5 3 A₁ (9,6) 9 X Q shown in the following figure. Ⓒ We compute the integral as the difference of the areas of the two triangles. √(x − 3) dx = A₁ - A₂ = -4.5=[ But, because y² = we get x² + y² = 25, which shows that the graph of f is the
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