The polynomial is considered on the interval

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

The polynomial f(x)=x2−4f(x)=x^{2}-4 is considered on the interval [−3,3][-3,3]. Which one of the following expressions must be evaluated to obtain the unsigned area enclosed between its graph and the xx-axis on this interval? (a) ∫−3−2(x2−4) dx+∫−22(x2−4) dx+∫23(x2−4) dx\displaystyle\int_{-3}^{-2}(x^{2}-4)\,dx+\int_{-2}^{2}(x^{2}-4)\,dx+\int_{2}^{3}(x^{2}-4)\,dx (b) ∫−3−2(x2−4) dx+∫−22(4−x2) dx+∫23(x2−4) dx\displaystyle\int_{-3}^{-2}(x^{2}-4)\,dx+\int_{-2}^{2}(4-x^{2})\,dx+\int_{2}^{3}(x^{2}-4)\,dx (c) ∫−3−2(4−x2) dx+∫−22(x2−4) dx+∫23(4−x2) dx\displaystyle\int_{-3}^{-2}(4-x^{2})\,dx+\int_{-2}^{2}(x^{2}-4)\,dx+\int_{2}^{3}(4-x^{2})\,dx (d) 2∫02(4−x2) dx\displaystyle 2\int_{0}^{2}(4-x^{2})\,dx

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