Answer to Question #100024 in Calculus for Jeffrey Chen

Question #100024
1. Find the area between the curves y= x^2-3x and y=x.
1
Expert's answer
2019-12-09T06:04:24-0500

First let's find the intersection points of these curves

x23x=x    x24x=0x^2-3x=x\iff x^2-4x=0

x=0;x=4x=0;\quad x=4

The area between these curves can be found as a Riemann integral

S=04(x24x)dx=(x332x2)04=64332=323S=\left|\int\limits_0^4(x^2-4x)dx\right|=\left|\left(\frac{x^3}{3}-2x^2\right)_0^4\right|=\left| \frac{64}{3}-32\right|=\frac{32}{3}


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