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Question:

Let I = ∫ba (x⁴ - 2x²) dx. If I is minimum, then the ordered pair (a, b) is?

(√2, -√2)

(0, √2)

(-√2, 0)

(-√2, √2)

Solution:

Let f(x) = x²(x² - 2) = x²(x - √2)(x + √2)
As long as f(x) lies below the x-axis, the definite integral will remain negative, so the correct value of (a, b) is (-√2, √2) for the minimum of I.