Mathematics, 06.05.2020 02:20, joheste2831
What is the area of the region between the graphs of f(x) = x^2 + 2xf(x) = x2 +2x, and g(x) = 2x+1g(x) = 2x+1g(x) = 2x + 1?
Answers: 3
![A = \int\limits^a_b {( y_2 (x) - y_1(x) )} \, dx \\\\y_2 ( x ) y_1 ( x )\\\\A = \int\limits^a_b {( g (x) - f(x) )} \, dx \\\\A = \int\limits^a_b {( x^2 + 2x - 2x - 1 )} \, dx \\\\ A = \int\limits^a_b {( x^2 - 1 )} \, dx \\\\A = [ \frac{x^3}{3} - x ]\limits^1_-_1 \\\\A = [ \frac{1^3}{3} - 1 - \frac{(-1)^3}{3} - (-1) ]\\\\A = [ \frac{1}{3} - 1 + \frac{1}{3} +1 ] = \frac{2}{3}](/tpl/images/0645/1866/85ded.png)
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What is the area of the region between the graphs of f(x) = x^2 + 2xf(x) = x2 +2x, and g(x) = 2x+1g(...
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