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How do you find the antiderivative of #f(x)=sqrt3(x^2)#?

Answer 1

Emilia Aguilar

It is #x^3/sqrt3#

If F(x) is the antiderivative of f(x) then

#F(x)=intf(x)dx=>F(x)=intsqrt3*x^2dx=sqrt3*intx^2dx=sqrt3*x^3/3=x^3/sqrt3#

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Answer 2

Charles Anctil

To find the antiderivative of ( f(x) = \sqrt{3}x^2 ), you can use the power rule for integration. The power rule states that the antiderivative of ( x^n ) with respect to ( x ) is ( \frac{x^{n+1}}{n+1} + C ), where ( C ) is the constant of integration. Applying this rule to ( f(x) = \sqrt{3}x^2 ), where ( n = 2 ), you get:

[ \int \sqrt{3}x^2 , dx = \frac{\sqrt{3}x^{2+1}}{2+1} + C ] [ = \frac{\sqrt{3}x^3}{3} + C ]

So, the antiderivative of ( f(x) = \sqrt{3}x^2 ) is ( \frac{\sqrt{3}x^3}{3} + 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.