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How do you find the antiderivative of #f(x)=4x^2-6x+7#?

Answer 1

Emma Aldridge

#int f(x) dx = 4/3x^3-3x^2+7x+C#

#f(x) = 4x^2-6x+7#

#int f(x) dx = int (4x^2-6x+7)dx#

#= 4*int x^2 dx -6* int xdx+7* int 1dx#

Applying the power rule to each term:

#= (4x^3)/3 - (6x^2)/2 +(7x^1)/1 +C#

#= 4/3x^3-3x^2+7x+C#

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Answer 2

Luke Alvarez

To find the antiderivative of ( f(x) = 4x^2 - 6x + 7 ), you can use the power rule for integration. The antiderivative of ( x^n ) is ( \frac{x^{n+1}}{n+1} ), where ( n ) is any real number except for ( -1 ). Applying this rule to each term individually:

[ \int 4x^2 , dx = \frac{4x^3}{3} + C ] [ \int -6x , dx = -3x^2 + C ] [ \int 7 , dx = 7x + C ]

Where ( C ) is the constant of integration. So, the antiderivative of ( f(x) = 4x^2 - 6x + 7 ) is:

[ \frac{4x^3}{3} - 3x^2 + 7x + C ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.