MAT136H1 Lecture Notes - Antiderivative
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MAT136H1 Full Course Notes
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Check if only one end is infinity or two. If one end is infinity, also check if the other interval end affects the denominator function if there is one. Then convert the integral by adding limit as . Variable is used for no other reason than that variable is already taken for the function in the integral. Proceed to take the anti-derivative disregarding the limit at first. After the integral is evaluated, plug in the value that variable approaches. Then it should be clear whether the function is convergent or divergent! Determine if the integral is convergent or divergent. Since the upper end approaches infinity, convert the expression by adding the limit, so that: Then without worrying about the limit, take the anti-derivative of the function using all the techniques you know so far. Here, the function is in the form of chain rule, so substitution can be used.