Integrate e^(x) from 1 to 2: animated lesson

1. 1. The problem
   Evaluating an integral

   $\int_{1}^{2} {e}^{x}\,dx$
2. 2. Step by step
   1. $$\int_{1}^{2} {e}^{x}\,dx$$
      Start with the definite integral
   2. $$\int {e}^{x}\,dx = {e}^{x}$$
      Exponential rule: ∫ eᵘ du = eᵘ (divide by the inner slope)
   3. $$F(x) = {e}^{x}$$
      Antiderivative
   4. $$F(2) - F(1) = 7.389056099 - 2.718281828 = 4.67077427$$
      Apply the fundamental theorem of calculus
3. 3. The answer
   $$\int_{1}^{2} {e}^{x}\,dx = 4.67077427$$

   ∫ from 1 to 2 = 4.67077427

4. 4. Check
   • ✓Differentiated the antiderivative and compared it with the integrand ✓
   • ✓Adaptive Simpson's rule gives 4.67077427 ✓

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