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Introduction to integration

Calculating definite integrals

The rule to finding the definite integral is:

$\int^b_a f(x) \; \mathrm{d}x = \Big[F(x)\Big]^b_a = F(b)-F(a)$

For example evaluate the definite integrals:

1. $$\displaystyle \int^4_1\left(\frac{1}{x} + \frac{1}{\sqrt{x}}\right) \; \mathrm{d}x$$
2. $$\displaystyle \int^{\pi/2}_0(\cos \theta + \sin \theta) \; \mathrm{d}\theta$$