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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

Let f(x) = x^2 + 2x - t^2 and f(x) = 0 has two roots (t) and (t)( < ) where t is a real parameter. Let I(t) = _ ^ f(x) dx . If the maximum value of I(t) be and | | = p q where p and q are relatively prime positive integers. Find the product (pq) .

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