What is the method for evaluating integrals with linear terms?

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SUMMARY

The method for evaluating integrals with linear terms involves splitting the limits of integration into intervals where the integrand maintains a consistent sign. For the integral of the function defined by the product of linear terms x(x-5)(x+7), the critical points are x = -7, x = 0, and x = 5. The integral should be broken into two parts: from -7 to 0 and from 0 to 5, calculating each integral separately while considering the sign of the integrand in each interval, and then summing the results.

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maobadi
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Evaluate the integral
integral.jpg
 
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Hi maobadi! :smile:

Split the limits of integration into two or more intervals on each of which the integrand has the same sign, so that, on each interval, you can replace || by either +() or -() :wink:
 
Since the quantity inside the absolute value sign is a product of linear terms, x(x-5)(x+7), it is easy to see that it is 0 exactly at x= -7, x= 0, and x= 5. Break the integral into two parts, from -7 to 0 and from 0 to 5, do those integrals separately (being careful about the sign) and add the results.
 

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