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How do you find the area between #f(x)=x^2-4x, g(x)=0#?

1 Answer

Apr 18, 2017

Area: #32/3 =10 2/3# square units.

Explanation:

Note that #f(x)# and #g(x)# intersect when #f(x)=g(x)#
#rarr f(x)=x^2-4x=0color(white)("xxx")x in {0,4}#

enter image source here

The area enclosed by #f(x)# and #g(x)# is therefore
#abs(int_0^4(f(x)-g(x)) dx)#

#color(white)("XXX")=abs(int_0^4 (x^2-4x) dx)#

#color(white)("XXX")=abs(color(white)("x")((x^3)/3-2x^2)"]"_0^4)#

#color(white)("XXX")=abs(64/3-32)#

#color(white)("XXX")=32/3#

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