A continuous function is defined on

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A continuous function pp is defined on [0,10][0,10]. A partially completed data table of its definite integrals is shown below.
IntegralReported value
∫04p(x) dx\displaystyle\int_{0}^{4} p(x)\,dx77
∫47p(x) dx\displaystyle\int_{4}^{7} p(x)\,dx−3-3
∫010p(x) dx\displaystyle\int_{0}^{10} p(x)\,dx  ?  \;?\;
∫710p(x) dx\displaystyle\int_{7}^{10} p(x)\,dx  2\;2
Answer the following. (1) Determine the missing value ∫010p(x) dx\displaystyle\int_{0}^{10} p(x)\,dx. Show your calculation clearly. (2) Verify that your result is consistent by calculating ∫100p(x) dx\displaystyle\int_{10}^{0} p(x)\,dx and explaining how its numerical value relates to the one you found in part (a).

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