For the function

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

For the function p(x)=5(x−2)(x+1)p(x)=\dfrac{5}{(x-2)(x+1)}, define two definite integrals: I1=∫−11p(x) dxI_1=\displaystyle \int_{-1}^{1} p(x)\,dx, I2=∫35p(x) dxI_2=\displaystyle \int_{3}^{5} p(x)\,dx. (1) Part 1: Determine the exact value of I1I_1. (2) Part 2: Determine the exact value of I2I_2. (3) Part 3: Using your answers to parts (a) and (b), decide which integral has the greater absolute value. Explain your reasoning in the context of the sign of p(x)p(x) over each interval.

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