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How do you integrate #int (root3x)#?

Answer 1

Luke Alvarez

#int root(3)x dx = 3/4 xroot(3)x +C#

The power rule can be applied to integration:

#int x^alpha dx = x^(alpha+1)/(alpha+1) + C#

In our instance:

#int root(3)x dx = int x^(1/3)dx = x^(4/3)/(4/3) + C = 3/4 xroot(3)x +C#

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Answer 2

Isabella Ackerman

To integrate ( \sqrt{3x} ), use the power rule for integration:

[ \int \sqrt{3x} , dx = \frac{2}{3} (3x)^{\frac{3}{2}} + C = 2x\sqrt{3x} + 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.