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

1 Answer
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)