Mathematics

Mathematics

Problem

The curve x2+y2=25x^{2}+y^{2}=25 is a circle of radius 55. To obtain the exact area of its upper semicircle using a definite integral, which one of the following integrals is appropriate? a) ∫−5525−x2 dx\displaystyle \int_{-5}^{5} \sqrt{25-x^{2}}\,dx b) ∫0525−x2 dx\displaystyle \int_{0}^{5} \sqrt{25-x^{2}}\,dx c) ∫−55(25−x2) dx\displaystyle \int_{-5}^{5} (25-x^{2})\,dx d) ∫0π25 dθ\displaystyle \int_{0}^{\pi} 25\,d\theta

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