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What is the difference between definite and indefinite integrals?

Answer 1

Indefinite integrals have no lower/upper limits of integration. They are general antiderivatives, so they yield functions.

#int f(x) dx=F(x)+C#,

where #F'(x)=f(x)# and #C# is any constant.

Definite integrals have lower and upper limits of integration (#a# and #b#). They yield values.

#int_a^b f(x) dx = F(b)-F(a)#,

where #F'(x)=f(x)#.

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Answer 2

Christopher Allers

The definite integral calculates the area under a curve between two specific points on the x-axis, while the indefinite integral finds a function's antiderivative without specifying limits 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.