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.