Integral Math Example 2

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Example 2

medium
Evaluate ∫02(3x2+1) dx\int_0^2 (3x^2 + 1) \, dx

Solution

  1. 1
    Find the antiderivative: F(x)=x3+xF(x) = x^3 + x.
  2. 2
    Apply the Fundamental Theorem of Calculus: ∫02f(x) dx=F(2)−F(0)\int_0^2 f(x)\,dx = F(2) - F(0).
  3. 3
    Evaluate: F(2)=8+2=10F(2) = 8 + 2 = 10 and F(0)=0+0=0F(0) = 0 + 0 = 0.
  4. 4
    Result: 10−0=1010 - 0 = 10.

Answer

1010
The Fundamental Theorem of Calculus connects antiderivatives to definite integrals. Find the antiderivative, then evaluate at the upper and lower bounds and subtract.

About Integral

The reverse operation of differentiation; it also computes the exact area under a curve between two points.

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