how can i solve this problem and plotting?

x=1:1:50;
plot x,a grap?

Answer 1

[Alan Stevens]

I assume you want to find the values of a that make the integral = 75, for all values of x. if so, then the following should do it:

x = 1:50;
aguess = 50;
for i = 1:50
    a(i) = fzero(@(a) fn(a,x(i)),aguess);
    aguess = a(i);
end
plot(x,a,'o'),grid
xlabel('x'),ylabel('a')

function z = fn(a,x)
        f = @(x) sqrt(1+(2*a*x).^2);
        z = integral(f,0,x)-75;
end

Note that the a's found from the above are positive, but the negative equivalents would also work, because a is squared in the integral.

[burak yilmaz]

I’m so grateful for your help. Thank you.