MATH1151 Chapter Notes - Chapter 5: Improper Integral, Upper And Lower Bounds
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Find i = z x sin x dx. [think: differentiating x makes it simpler; integrating sin x doesn"t make it worse. ] Let u = , u 0 = , v 0 = v = = x cos x +z cos x dx (which can easily be checked by differentiating the answer!) It is less obvious here to choose: u = u 0 = , v 0 = , v = . Does it make any sense to talk about the area" in the rst quadrant underneath the graph of y = e x ? y e x x. We can"t do what we did before because you can"t possibly t this unbounded region inside a nite union of polygons. On the other hand, there is a limit to the total area of any polygons that you could ever put inside the region. This is roughly the idea behind the following de nition: definition.
