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Category: Integration

let-f-a-dx-x-2-1-a-e-ix-with-a-gt-0-1-find-a-explicit-form-of-f-a-2-determine-also-g-a-dx-x-2-1-a-e-ix-2-3-let-I-Re-dx-

Question Number 67542 by mathmax by abdo last updated on 28/Aug/19 letf(a)=+dx(x2+1)(a+eix)witha>01)findaexplicitformoff(a)$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({a}\right)=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({a}+{e}^{{ix}} \right)^{\mathrm{2}} }…

Suppose-0-lt-b-a-Show-that-the-area-of-intersection-E-F-of-the-two-regions-defined-by-E-x-y-x-2-a-2-y-2-b-2-1-and-F-x-y-x-2-b-2-y-2-a-2-1-is-4absin-1-b-a-2-b-2-

Question Number 2004 by Yozzi last updated on 29/Oct/15 Suppose0<ba.ShowthattheareaofintersectionEFofthetworegionsdefinedbyE={(x,y):x2a2+y2b21}and$${F}=\left\{\left({x},{y}\right):\frac{{x}^{\mathrm{2}} }{{b}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{a}^{\mathrm{2}}…