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Category: Integration

find-I-D-1-x-2-a-2-y-2-b-2-dxdy-with-D-is-the-interior-of-ellipce-x-2-a-2-y-2-b-2-1-

Question Number 30569 by abdo imad last updated on 23/Feb/18 $${find}\:{I}=\:\int\int_{{D}} \:\sqrt{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }−\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }}\:\:{dxdy}\:\:{with}\:{D}\:{is}\:{the}\:{interior} \\ $$$${of}\:{ellipce}\:\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:=\mathrm{1}. \\ $$ Terms…

f-and-g-are-2-function-C-n-on-a-b-prove-that-a-b-f-n-x-g-x-dx-k-0-n-1-1-k-f-k-g-n-k-a-b-1-n-a-b-f-x-g-n-x-dx-

Question Number 30564 by abdo imad last updated on 23/Feb/18 $${f}\:{and}\:{g}\:{are}\:\mathrm{2}\:{function}\:\:{C}^{{n}} \:{on}\:\left[{a},{b}\right]\:{prove}\:{that} \\ $$$$\int_{{a}} ^{{b}} \:{f}^{\left({n}\right)} \left({x}\right){g}\left({x}\right){dx}=\left[\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left(−\mathrm{1}\right)^{{k}} \:{f}^{\left({k}\right)} {g}^{\left({n}−{k}\right)} \right]_{{a}} ^{{b}} \:+\left(−\mathrm{1}\right)^{{n}} \int_{{a}}…

Question-96097

Question Number 96097 by mhmd last updated on 29/May/20 Answered by mathmax by abdo last updated on 29/May/20 $$\mathrm{A}\:=\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\left(\mathrm{e}^{\mathrm{x}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)}\:\mathrm{changement}\:\mathrm{x}=−\mathrm{t}\:\mathrm{give} \\ $$$$\mathrm{A}\:=−\int_{−\mathrm{1}}…