Find the Definite Integral of Arccos Function in Matlab | Integral Problem

[amykelly36]

I want to find the definite integral of

arccos(sqrt(1+x)/10)/(sqrt(x)*x^(2/3))​

,over [0,pi/2].

I ran the following code in Matlab,

"syms w

double(vpa(int(acos((w + 1)^(1/2)/10)/(w^(1/2)*(w + 1)^(3/2)),w,0,pi/2)))"

and got this error message,

"? Error using ==> mupadmex
Error in MuPAD command: DOUBLE cannot convert the input expression into a
double array.

If the input expression contains a symbolic variable, use the VPA function
instead.

Error in ==> sym.sym>sym.double at 936
Xstr = mupadmex('symobj::double', S.s, 0);

Error in ==> HW at 4
double(vpa(int(acos((w + 1)^(1/2)/10)/(w^(1/2)*(w + 1)^(3/2)),w,0,pi/2)))".

Anybody has met such situation like me before? I appreciate any comment!

 

[Undoubtedly0]

Hello there! I think that int() cannot be used here, since the integral will need to be evaluated numerically. Try using quadl() instead:

this = @(w)acos((w+1).^(1/2)/10)./(w.^(1/2).*(w+1).^(3/2)); % note the elementwise operations (.^, ./, .*)

quadl(this,0,pi/2)

Hopefully that helps!

 

[amykelly36]

Thanks a lot! It exactly settles the issue.