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Compute an integral of (x-1)(3x-1)

Compute

    \[ \int_0^2 (x-1)(3x-1) \, dx. \]


We expand and use the formula for integral of a polynomial to compute,

    \[ \int_0^2 (x-1)(3x-1) \, dx = \int_0^2 (3x^2 - 4x + 1) \, dx = \left. \left( 3 \frac{x^3}{3} - 4 \frac{x^2}{2} + x \right) \right|_0^2 = (8 - 8 + 2) - 0 = 2. \]

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