The Definite Integral as Area

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1. 1. The question0:00

2. 2. Antiderivative0:14
   1. $$\int_0^2 (x^2 + 1)\,dx$$
   2. $$F(x) = \frac{x^3}{3} + x$$
3. 3. Fundamental Theorem0:24
   1. $$F(2) - F(0)$$
   2. $$= \left(\frac{8}{3} + 2\right) - 0$$
   3. $$= \frac{14}{3} \approx 4.67$$
4. 4. Recap0:40
   • ✓Find any antiderivative $F$.
   • ✓$\int_a^b f(x)\,dx = F(b) - F(a)$.
   • ✓Above the axis, the integral is the area.

Antiderivatives, substitution and the Fundamental Theorem.

• Integral Calculator: try the same kind of problem with your own numbers.
• Definite Integral Calculator: try the same kind of problem with your own numbers.
• More calculus practice problems
• Limits Study Guide (study guide)
• AP Calculus AB Unit 6: Integration and Accumulation of Change: the AP unit this lesson supports.
• Calculus calculators and topics
• Step-by-step solver: check your own answer with hints.

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