Integrate e^x from 0 to 1: animated lesson

1. 1. The problem
   Evaluating an integral

   $\int_{0}^{1} {e}^{x}\,dx$
2. 2. Step by step
   1. $$\int_{0}^{1} {e}^{x}\,dx$$
      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. $$F(1) - F(0) = 2.718281828 - 1 = 1.718281828$$
      Apply the fundamental theorem of calculus
3. 3. The answer
   $$\int_{0}^{1} {e}^{x}\,dx = 1.718281828$$

   ∫ from 0 to 1 = 1.718281828

4. 4. Check
   • ✓Differentiated the antiderivative and compared it with the integrand ✓
   • ✓Adaptive Simpson's rule gives 1.718281828 ✓

Evaluate definite integrals with the fundamental theorem of calculus.

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