I am working on a line integral to calculate the amount of chocolate to cover a pretzel. the density of the pretzel is given by this formula $\lambda=3(x^2+y^2)$ and the parameter equation of a pretzel shape is given by
$$x(t)=-4\sin 3t \quad\text{and}\quad y(t)=4\cos4t$$
apply the mass formula $\int_C \rho (x,y)\,ds$
I get
$$\int_0^{2\pi}\left((16\sin^2 3t +16\cos^2 4t)\sqrt{144\cos^2 3t +256\sin^2 4t}\right) \,dt$$
then I have no idea how calculate this line integral.
can anyone give me a hint? Thanks!