Discussion 2A & 2B.docx

Discussion 2A & 2B.docx - Discussion 2A Explain what an...

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Discussion 2A Explain what an improper integral is and provide an example. What techniques are available in helping us evaluate improper integrals? Improper integral is known as the definite integral when the upper and lower boundaries go to infinity. This means that the limits of the integral approach infinity either at a point ( ∞,b ] [ a,∞ ) or more points (− ∞,∞ ) . The limits of integral also can approach infinity when the integrand has a vertical asymptote in the interval of the integration. For example, the boundaries are [-1,3] or we can write as 1 3 f ( x ) . At the graph, there is vertical asymptote in between 1 and 3 (in this case we assume that the vertical asymptote is in x = 0), then, the graph of [-1,0) will turn so as not to pass vertically asymptote, then the limit of the integrand will be [-1, ∞) and so will the graph from the interval across it. For example, if we have f ( x ) = 1 x 2 , then we are asked to calculate the integral of f(x) at the boundaries from 1 to ∞. For this problem, we can use
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