Evaluate the following integrals by interpreting each in terms of areas.√ √ 25-x² dx(a)(b) f(x-(x-3) dxSolution(a) Since f(x) = √25-²20, we can interpret this integral as the area under the curve y = √25-2 from 0 toquarter-circle with radius 5✔✔ in the figure below.yy=√√25-x²orx² + y² = 25Therefore, •6² √25-x² dx = = m(5)² =y5(b) The graph of y=x-3 is the line with slope 22.5(x-3) dx = A₁ - A₂ =25x(9,6)y = x-3ÀA₁9A₂-X shown in the following figure.XWe compute the integral as the difference of the areas of the two triangles.f (x-3) d4.5 = 22.5 x .. But, because y²=, we get x² + y² = 25, which shows that the graph of f is the

Let Equation (1) represents the circle of radius 5 unitsThe area of quadrants is given as,

Evaluate the following integrals by interpreting each in terms of areas. (0) S√25-x² dx (b) √(x-3) dx Solution (a) Since f(x)=√25-²20, we can interpret this integral as the area under the curve y= √25-x² from 0 to [ quarter-circle with radius [5✔ in the figure below. Therefore,√25-²dx=(5)² = A₂ y=√√25-x² or x² + y² = 25 y x-3 5 3 (b) The graph of y=x-3 is the line with slope 22.5 X shown in the following figure. A₁ 257 (9,6) 9 ℗ X Q We compute the integral as the difference of the areas of the two triangles. f(x-3) dx = A₁ - A₂ - [ -4.5-22.5 x . But, because y² = x we get x² + y² = 25, which shows that the graph of fis t

Evaluate the following integrals by interpreting each in terms of areas. (0) S√25-x² dx (b) √(x-3) dx Solution (a) Since f(x)=√25-²20, we can interpret this integral as the area under the curve y= √25-x² from 0 to [ quarter-circle with radius [5✔ in the figure below. Therefore,√25-²dx=(5)² = A₂ y=√√25-x² or x² + y² = 25 y x-3 5 3 (b) The graph of y=x-3 is the line with slope 22.5 X shown in the following figure. A₁ 257 (9,6) 9 ℗ X Q We compute the integral as the difference of the areas of the two triangles. f(x-3) dx = A₁ - A₂ - [ -4.5-22.5 x . But, because y² = x we get x² + y² = 25, which shows that the graph of fis t

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.

Chapter8: Further Techniques And Applications Of Integration

Section8.2: Integration By Parts

Problem 36E

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