Evaluate the line integral ∫cf⋅dr, where f(x,y,z)=−4xi−3yj+4zk and c is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.

[tex]\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r[/tex]
[tex]=\displaystyle\int_{t=0}^{t=3\pi/2}\mathbf f(\sin t,\cos t,t)\cdot\langle\cos t,-\sin t,1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{3\pi/2}\langle-4\sin t,-3\cos t,4t\rangle\cdot\langle\cos t,-\sin t,1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{3\pi/2}(4t-\cos t\sin t)\,\mathrm dt=\dfrac{9\pi^2-1}2[/tex]