Find ∫₀³ x² dx
Compute a definite integral with the fundamental theorem of calculus.
Solution
- Integrand f(x) = x²
- Reverse power rule ∫ 1x² dx = 0.333333x³
- Indefinite integral ∫ f(x) dx = 0.333333x³ + C
- Evaluate F(b) F(3) = 9
- Evaluate F(a) F(0) = 0
- Definite integral F(b) − F(a) = 9
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