Integrate cos(x) from -3 to 0: animated lesson

1. 1. The problem
   Evaluating an integral

   $\int_{-3}^{0} \cos\left( x\right)\,dx$
2. 2. Step by step
   1. $$\int_{-3}^{0} \cos\left( x\right)\,dx$$
      Start with the definite integral
   2. $$\int \cos\left( x\right)\,dx = \sin\left( x\right)$$
      ∫ cos x dx = sin x
   3. $$F(x) = \sin\left( x\right)$$
      Antiderivative
   4. $$F(0) - F(-3) = 0 - \left(-0.1411200081\right) = 0.1411200081$$
      Apply the fundamental theorem of calculus
3. 3. The answer
   $$\int_{-3}^{0} \cos\left( x\right)\,dx = 0.1411200081$$

   ∫ from -3 to 0 = 0.1411200081

4. 4. Check
   • ✓Differentiated the antiderivative and compared it with the integrand ✓
   • ✓Adaptive Simpson's rule gives 0.1411200081 ✓

Evaluate definite integrals with the fundamental theorem of calculus.

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