hind

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These are questions asked by hind

How integrate this function 

``

int((1/2)/(s^(1/2)*GAMMA(1/2)*(t^(1/2)-s^(1/2)))*(s^6), s = 0 .. t);

signum(t)^6*infinity

(1)

``

``

Thank you for helpping

Download qu_integral.mwqu_integral.mw


what is the reason for negative value is displayed on the table? 

thank you for helping>>>>>mapel_prime.mw

How to find the value of alpha and beta?

restart

u := proc (x) options operator, arrow; sin(x)+cos(x)-4*x+(alpha-4)*x end proc; v := proc (x) options operator, arrow; sin(x)-cos(x)+beta end proc; `assuming`([solve({alpha = int(u(t)+v(t), t = 0 .. Pi), beta = int(u(t)-v(t), t = 0 .. Pi)}, {alpha, beta})], [alpha <> 0, beta <> 0])

{alpha = 4+beta*Pi+(1/2)*alpha*Pi^2-4*Pi^2, beta = -beta*Pi+(1/2)*alpha*Pi^2-4*Pi^2}

(1)

``

thank you for helping

Download Qu_3.mw

How evaluate system of two integral equation by laplace transform ?

 

with(inttrans):

L := laplace((1/2)*x^2+(1/2)*x^3+(1/12)*x^4 = int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s);

(s^2+3*s+2)/s^5 = laplace(int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s)

 

(3*s^2-s+2)/s^5 = laplace(int((1+x-t)*u(t)+(-1+x-t)*v(t), t = 0 .. x), x, s)

(1)

``

 

Download Qu_2_mapel.mwQu_2_mapel.mw

How plot two functions of two variables to (2-dimension)?

restart;
approximate := exp(-2*t)+x*exp(-2*t)+(1/2)*exp(-2*t)*x^2+(1/6)*exp(-2*t)*x^3+(1/24)*exp(-2*t)*x^4+(1/120)*exp(-2*t)*x^5+(1/720)*exp(-2*t)*x^6+(1/5040)*exp(-2*t)*x^7+(1/40320)*exp(-2*t)*x^8+(1/362880)*exp(-2*t)*x^9+(1/3628800)*exp(-2*t)*x^10+(1/39916800)*exp(-2*t)*x^11+(1/479001600)*exp(-2*t)*x^12+(1/6227020800)*exp(-2*t)*x^13+(1/87178291200)*exp(-2*t)*x^14+(1/1307674368000)*exp(-2*t)*x^15+(1/20922789888000)*exp(-2*t)*x^16+(1/355687428096000)*exp(-2*t)*x^17+(1/6402373705728000)*exp(-2*t)*x^18+(1/121645100408832000)*exp(-2*t)*x^19+(1/2432902008176640000)*exp(-2*t)*x^20+(1/51090942171709440000)*exp(-2*t)*x^21;
apr := unapply(approximate, x, t);
Exact := (x, t)-> exp(x-2*t) ;
plot3d(exp(x-2*t)-approximate, x = 0 .. 5, t = 0 .. 5);

 

plot.mw

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