We noticed that this didnt give a very good approximation unle the number of

# We noticed that this didnt give a very good

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axis. We noticed that this didn’t give a very good approximation unless the number of rectangles was rather large. It should be clear from the rectangular representation of the area, that we could do better in estimating the area if we formed trapezoids using both sides of the interval. This should give a better approximation.
5.7 - The natural logarithm - Integration Objectives 1. Use the Log Rule for Integration to integrate a rational function 2. Integrate Trigonometric Functions We know how to differentiate a logarithm. We can also use the definition in a slightly modified form to integrate functions involving fractions: Log Rule: integraltext 1 x dx = ln | x | + C General Log Rule: integraltext 1 u du = ln | u | + C So we want to get used to sometimes letting u be the denominator of a fraction, and hope that the numerator gives us the du that we need. Example: Find integraldisplay x x 2 + 1 dx Find integraldisplay 3 x + 1 dx Find integraldisplay 2 1 - 3 x dx
5.8 - Inverse Trig Functions - Integration Objectives