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What is #int_(0)^(2) x^(3)dx #?

Answer 1

4 sq units

Remember that an application of integration is to find the area under a curve. In this example you are finding the area bounded between 0 and 2.

First you apply the integration rules.

#int x^3dx=(x^4)/4#

Now apply the bounds of 0 and 2.

#[(x^4)/4]_0^2#

Substitute in the upper bound into the expression Substitute in the lower bound into the expression Subtract the lower bound result from the upper bound result

#[(x^4)/4]_0^2=(2^4)/4-(0^4)/4=16/4-0=16/4=4# square units

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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.