Question: integral of solution of differential equation

Hi all,

I have a differential equation as follows:

x(t)^2+cos(x(t))+diff(x(t), t)+diff(x(t), t, t) = 100

x(0)=2, D(x)(0) = 3;

After using "dsolve" to solve this equation, the solution x(t) is obtained.

How can we obtain the following function?

g(k) = 0kx2(t)dt

How can we plot the function g(k) when k = 0 ..10?

I tried many ways, but I'm only able to obtain the derivative of x(t), not the integral of x2(t). My Maple file is attached in this post.

Thank you so much. 


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