Definite Integral Math Example 1

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Example 1

easy
Evaluate ∫14(2x−1) dx\int_1^4 (2x - 1)\,dx.

Solution

  1. 1
    Find the antiderivative: F(x)=x2−xF(x) = x^2 - x.
  2. 2
    Apply the Fundamental Theorem: ∫14(2x−1) dx=F(4)−F(1)\int_1^4 (2x-1)\,dx = F(4) - F(1).
  3. 3
    Compute F(4)=16−4=12F(4) = 16 - 4 = 12 and F(1)=1−1=0F(1) = 1 - 1 = 0.
  4. 4
    Result: 12−0=1212 - 0 = 12.

Answer

1212
For a definite integral, find the antiderivative, evaluate it at the upper bound, then subtract its value at the lower bound. The constant of integration cancels out when you subtract, so it can be omitted.

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 2 medium

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

Example 3 easy

Evaluate [formula].

Example 4 hard

Evaluate [formula] and explain the geometric meaning.

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