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Author: Tinku Tara

Solve-integral-of-sec-x-dx-given-that-t-tan-x-2-

Question Number 5866 by sanusihammed last updated on 02/Jun/16 $${Solve}\:{integral}\:{of}\:\:\:{sec}\left({x}\right){dx}\:\:.\:\:{given}\:{that}\:\:{t}\:=\:{tan}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$ Answered by Yozzii last updated on 02/Jun/16 $${Let}\:{t}={tan}\mathrm{0}.\mathrm{5}{x}\Rightarrow{dt}=\mathrm{0}.\mathrm{5}{sec}^{\mathrm{2}} \mathrm{0}.\mathrm{5}{xdx} \\ $$$${dx}=\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} } \\…

cos-x-e-cos-x-sin-x-dx-

Question Number 136935 by metamorfose last updated on 27/Mar/21 $$\int{cos}\left({x}\right){e}^{{cos}\left({x}\right)+{sin}\left({x}\right)} {dx}=…? \\ $$ Answered by liberty last updated on 27/Mar/21 $$\int\:\mathrm{cos}\:\mathrm{x}.\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} .\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} \:\mathrm{dx}\:= \\ $$$$\mathrm{by}\:\mathrm{parts}…

e-ln-sin-1-x-1-x-2-dx-

Question Number 136929 by liberty last updated on 27/Mar/21 $$\int\:\frac{\mathrm{e}^{\mathrm{ln}\:\left(\mathrm{sin}^{−\mathrm{1}} \mathrm{x}\right)} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 27/Mar/21 $$\int\frac{{e}^{{log}\left({sin}^{−\mathrm{1}} {x}\right)}…

what-is-the-intutive-understanding-of-eigenvalues-and-vectors-with-practical-examples-

Question Number 5859 by wanderer last updated on 02/Jun/16 $${what}\:{is}\:{the}\:{intutive}\:{understanding}\:{of}\: \\ $$$${eigenvalues}\:{and}\:{vectors}.{with}\:{practical}\: \\ $$$${examples}. \\ $$ Commented by FilupSmith last updated on 02/Jun/16 $$\mathrm{A}\:\mathrm{vector}\:\mathrm{is}\:\mathrm{a}\:\mathrm{direction}\:\mathrm{and}\:\mathrm{magnitude}. \\…