MATH 132, section 1 – Calculus for Physical and Life Sciences First Integration Examples January 22, 2008

The Evaluation Theorem for integrals says: If f(x) is continuous on [a, b] and F (x) is any antiderivative of f(x), then

∫_{a}^{b} f(x) dx = F (x)|_{a}^{b} = F (b) − F (a).

For each of the following integrals, apply the Evaluation Theorem to find the value:

• ∫_{1}^{3} x^{1/3} − 3x dx

• ∫_{0}^{π/3} cos(x) dx

• ∫_{0}^{1} \frac{1}{1 + x^{2}} dx

• ∫_{1}^{5} \frac{1 + 6x + x^{2}}{x} dx

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