Integrate e^(x) from -2 to 0: animated lesson

1. 1. The problem
   Evaluating an integral

   $\int_{-2}^{0} {e}^{x}\,dx$
2. 2. Step by step
   1. $$\int_{-2}^{0} {e}^{x}\,dx$$
      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. $$F(0) - F(-2) = 1 - 0.1353352832 = 0.8646647168$$
      Apply the fundamental theorem of calculus
3. 3. The answer
   $$\int_{-2}^{0} {e}^{x}\,dx = 0.8646647168$$

   ∫ from -2 to 0 = 0.8646647168

4. 4. Check
   • ✓Differentiated the antiderivative and compared it with the integrand ✓
   • ✓Adaptive Simpson's rule gives 0.8646647168 ✓

Evaluate definite integrals with the fundamental theorem of calculus.

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