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Question Number 68033 Answers: 1 Comments: 0

find ∫ (dx/(1+sinx +sin(2x)))

$${find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{sinx}\:+{sin}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 68028 Answers: 0 Comments: 0

Question Number 68022 Answers: 1 Comments: 1

Question Number 68021 Answers: 1 Comments: 1

Question Number 68019 Answers: 0 Comments: 5

let F(x) =∫_x ^(x^2 +1) e^(−2t) sin(xt)dt determine F^′ (x) and calculate lim_(x→0) F(x).

$${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} +\mathrm{1}} {e}^{−\mathrm{2}{t}} {sin}\left({xt}\right){dt} \\ $$$${determine}\:{F}\:^{'} \left({x}\right)\:{and}\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}\left({x}\right). \\ $$$$ \\ $$

Question Number 68001 Answers: 0 Comments: 1

let F(x)=∫_(2x) ^(x^2 +1) (e^(−xt) /(x+2t))dt calculate F^′ (x)

$${let}\:{F}\left({x}\right)=\int_{\mathrm{2}{x}} ^{{x}^{\mathrm{2}} +\mathrm{1}} \:\:\frac{{e}^{−{xt}} }{{x}+\mathrm{2}{t}}{dt}\:\:\:\:{calculate}\:{F}\:^{'} \left({x}\right) \\ $$

Question Number 67997 Answers: 0 Comments: 0

5y^2 +2axy+b=0 ay^2 +2bx+5c=0 (5x+3a)y^2 +(4ax^2 )y−bx−5c=0 5y^2 −x(5x+2a)y−ax^3 −3b=0 Please solve simultaneously for x and y such that all four equations are obeyed.

$$\mathrm{5}{y}^{\mathrm{2}} +\mathrm{2}{axy}+{b}=\mathrm{0} \\ $$$${ay}^{\mathrm{2}} +\mathrm{2}{bx}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\left(\mathrm{5}{x}+\mathrm{3}{a}\right){y}^{\mathrm{2}} +\left(\mathrm{4}{ax}^{\mathrm{2}} \right){y}−{bx}−\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{5}{y}^{\mathrm{2}} −{x}\left(\mathrm{5}{x}+\mathrm{2}{a}\right){y}−{ax}^{\mathrm{3}} −\mathrm{3}{b}=\mathrm{0} \\ $$$${Please}\:{solve}\:{simultaneously} \\ $$$${for}\:{x}\:{and}\:{y}\:{such}\:{that}\:{all}\:{four} \\ $$$${equations}\:{are}\:{obeyed}. \\ $$

Question Number 67996 Answers: 1 Comments: 4

Question Number 67992 Answers: 1 Comments: 0

(1) z=a+bi (2) z=re^(iθ) express the values of (a) real (z^z ) [real part] (b) imag (z^z ) [imaginary part] (c) abs (z^z ) [absolute value] (d) arg (z^z ) [argument = angle]

$$\left(\mathrm{1}\right)\:{z}={a}+{b}\mathrm{i} \\ $$$$\left(\mathrm{2}\right)\:{z}={r}\mathrm{e}^{\mathrm{i}\theta} \\ $$$$\mathrm{express}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{real}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{real}\:\mathrm{part}\right] \\ $$$$\left(\mathrm{b}\right)\:\mathrm{imag}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{imaginary}\:\mathrm{part}\right] \\ $$$$\left(\mathrm{c}\right)\:\mathrm{abs}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{absolute}\:\mathrm{value}\right] \\ $$$$\left(\mathrm{d}\right)\:\mathrm{arg}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{argument}\:=\:\mathrm{angle}\right] \\ $$

Question Number 67991 Answers: 1 Comments: 1

Question Number 67983 Answers: 2 Comments: 1

Question Number 67977 Answers: 1 Comments: 1

Question Number 67974 Answers: 0 Comments: 2

let F(x) =∫_x ^x^2 ((arctan(xt))/(x^2 +t^2 ))dt calculate F^′ (x).

$${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{arctan}\left({xt}\right)}{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dt}\:\:{calculate}\:{F}\:^{'} \left({x}\right). \\ $$

Question Number 67973 Answers: 0 Comments: 5

Question Number 67972 Answers: 2 Comments: 0

if F(x)=∫_(u(x)) ^(v(x)) g(x,t)dt determine a expression for F^′ (x).

$${if}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\right)} {g}\left({x},{t}\right){dt}\:\:\:\:\:{determine}\:{a}\:{expression}\:{for}\:{F}\:^{'} \left({x}\right). \\ $$

Question Number 67969 Answers: 0 Comments: 0

Two triangles △_1 and △_2 are given,such that length of sides of triangle 1,are equail to length of medians of triangle 2. 1.find the ratio of areas of triangles. 2.given that small side of △_1 , be equail to:(√2) and one angle be:90^• . find at least one angle of △_2 . 3.solve part#2,if replace: △_2 with: △_1 . 4.solve part#2,if great side of:△_1 ,be equail to :(√2).

Question Number 67963 Answers: 1 Comments: 1