ONE
    Númas
    ← Back to the programme
    IBEasyCalculus10–12

    Area Under a Quadratic Between Two Limits

    Área Sob uma Quadrática Entre Dois Limites

    Evaluate \int_{1}^{3} (3x^{2} - 4x + 1)\,dx and state what the value represents for the curve y = 3x^{2} - 4x + 1 on that interval.

    Integrate term by term with the reverse of the power rule, then use the fundamental theorem. Before you claim the value is an area, ask whether the curve stays above the axis between the limits.

    Solution

    Step 1 of 7

    1. 1.Antiderivative: