From the picture attached how do you solve a problem like this please show steps 8765432A region is bounded by the x-axis and the graphs of y = ex, x = 0, and x = 2. The areaof the region isDOD

- For a curve having an equation y = f(x) and bounded by the x-axis and with limit values of a and…

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 61E

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To find the area of the shaded region, we need to compute the area for region A on the interval [0, 2] and the area for region B on the interval [2, 4], and then find the sum of the regions. y y =x - 2 x + 1 y=5- x For region A, the interval from [0, 2], notice that y = 5 - x is above the graph of y = x - 2x + 1, so the equations and limits of integration can be substituted into the area formula. Area = [f(x) – g(x)] dx [(5 – x3) – (x² – 2x + 1)] dx Area of A = substitute -2x² + 2x + dx distribute and combine like terms + x2 + 4x integrate - -2)? + (2)? + 4(2) - -0 - (o)? + 4co) %3D evaluate simplify Thus, the area of region A is square units.
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8 7 6 5 4 3 2 A region is bounded by the x-axis and the graphs of y = ex, x = 0, and x = 2. The area of the region is DOD