How do you solve for the limits of an integral?

Hi there

I am looking to solve the equation for PhetaS

W=b*r^(n+1)*(Kc/b+Kphi)*int((cos(Pheta)-cos(PhetaS))^n*cos(Pheta),Pheta,-PhetaS,PhetaS)

Where, W, b, r, n, Kc, Kphi are known values.

Below is the script I am using, however, I am having a lot of trouble:

clc; clear all; close all;
r=0.1; 
b=0.15;
Kc=0.99*1000;    Kphi=1528.4*1000;   n=1.1;    W=100;
syms Pheta PhetaS
f=W==(b*(Kc/b+Kphi)*r^(n+1))*int(((cos(Pheta)-cos(PhetaS))^n)*cos(Pheta),Pheta,-PhetaS,PhetaS)
solve(f,PhetaS)

Answer 1

[Walter Roberson]

r=0.1; 
b=0.15;
Kc=0.99*1000;    Kphi=1528.4*1000;   n=1.1;    W=100;
syms Pheta PhetaS
f=W==(b*(Kc/b+Kphi)*r^(n+1))*vpaintegral(((cos(Pheta)-cos(PhetaS))^n)*cos(Pheta),Pheta,-PhetaS,PhetaS)

f = 

vpasolve(f,PhetaS, .1)

ans = 

0.47873864697966172105256369269319

[Louis McDermott]

Thank you!