How do you find the antiderivative of #f(x)=2x^2-8x+2#?

1 Answer
Alan P.
Mar 1, 2017

#2/3x^3-4x^2+2x+C# for any constant #C#

Explanation:

Note that the antiderivative of #f(x)=p(x)+q(x)+r(x)#
is
the antiderivative of #p(x)#
plus the antiderivative of #q(x)#
plus the antiderivative of #r(x)#
plus a constant #color(red)(C)#

The derivative of #ax^b# is #b * a x^(b-1)#
From which we can see that:
The antiderivative of #cx^d# is #c/(d+1) * x^(d+1)#

Using this general form, we have
#color(white)("XXX")#antiderivative of #2x^2# is #color(red)(2/3 * x^3)#

#color(white)("XXX")#antiderivative of #-8x (=-8x^1)# is #(-8/2)x^(1+1)=color(red)(-4x^2)#

#color(white)("XXX")#antiderivative of #2 = 2 * x^0# is #(2/1) x^(0+1) = color(red)(2x)#

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