Definite Integral Math Example 3

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Example 3

easy
Evaluate ∫03x2 dx\int_0^3 x^2\,dx.

Solution

  1. 1
    Antiderivative: F(x)=x33F(x) = \frac{x^3}{3}.
  2. 2
    Apply FTC: F(3)−F(0)=273−0=9F(3) - F(0) = \frac{27}{3} - 0 = 9.

Answer

99
The power rule for integration gives x33\frac{x^3}{3}. Evaluating at x=3x=3 gives 99 and at x=0x=0 gives 00, so the definite integral equals 99.

About Definite Integral

An integral evaluated between specific bounds aa and bb, yielding a single number: the signed area under the curve.

Learn more about Definite Integral →

More Definite Integral Examples

Example 1 easy

Evaluate [formula].

Example 2 medium

Evaluate [formula] and interpret the sign of the result.

Example 4 hard

Evaluate [formula] and explain the geometric meaning.

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