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How do you find the antiderivative of #f(x)=3x^2+2#?

Answer 1

Charles Anctil

#int( 3x^2 + 2 ) dx = 3/3 x^3 + 2/1 x^1 + c#

For any indefinite integral, apply the reverse power rule and add a constant C at the end.

The reverse power rule states #int(x^2)dx = x^(2+1)/2#

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Answer 2

Cameron Alexander

To find the antiderivative of ( f(x) = 3x^2 + 2 ), you would apply the power rule for integration. The antiderivative of each term is found by adding 1 to the exponent and dividing by the new exponent.

So, the antiderivative of ( 3x^2 ) is ( x^3 ) and the antiderivative of ( 2 ) is ( 2x ).

Therefore, the antiderivative of ( f(x) = 3x^2 + 2 ) is ( F(x) = x^3 + 2x + C ), where ( C ) is the constant of integration.

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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.