One approach:
gamma = 4.2; % Create Parameter
resultOfIntegral = 42; % Create Value
intfcn = @(k,x) sqrt((1+k.*x.^2)./(1+gamma.*x.^2));
kv = fsolve(@(k) integral(@(x)intfcn(k,x),0,1) - resultOfIntegral, rand) % Integrate w.r.t. ‘x’ & Estimate ‘k’
Having the details always helps, however lacking them I created values to test the code.
