Mathematics

Mathematics

Problem

Let f(x)=x2−4f(x)=x^{2}-4 on the interval [−3,3][-3,3]. Which of the following expressions equals the total area of the region bounded by the graph of ff and the xx-axis on this interval? a) ∫−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 b) ∫−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 c) 2∫23(x2−4) dx\displaystyle 2\int_{2}^{3}(x^{2}-4)\,dx d) ∫−3−2(4−x2) dx+∫−22(4−x2) dx+∫23(4−x2) dx\displaystyle \int_{-3}^{-2}(4-x^{2})\,dx+\int_{-2}^{2}(4-x^{2})\,dx+\int_{2}^{3}(4-x^{2})\,dx

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