Mathematics

Mathematics

Problem

Which of the following definite integrals represents the volume of the solid whose base is the disk x2+y2≤16x^{2}+y^{2}\le 16 and whose cross sections perpendicular to the xx–axis are squares? a) ∫−44216−x2 dx\displaystyle \int_{-4}^{4}2\sqrt{16-x^{2}}\,dx b) ∫−44(216−x2)2 dx\displaystyle \int_{-4}^{4}\bigl(2\sqrt{16-x^{2}}\bigr)^{2}\,dx c) ∫04(216−y2)2 dy\displaystyle \int_{0}^{4}\bigl(2\sqrt{16-y^{2}}\bigr)^{2}\,dy d) ∫−44(16−x2)2 dx\displaystyle \int_{-4}^{4}\bigl(\sqrt{16-x^{2}}\bigr)^{2}\,dx

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