Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y) = xy i + 6y2 j r(t) = 16t6 i + t4 j, 0 ≤ t ≤ 1

[tex]\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\mathbf f(\mathbf r(t))\cdot\mathrm d(16t^6\,\mathbf i+t^4\,\mathbf j)[/tex]
[tex]=\displaystyle\int_0^1\bigg(16t^{10}\,\mathbf i+6t^8\bigg)\cdot\bigg(96t^5\,\mathbf i+4t^3\,\mathbf j\bigg)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(1536t^{15}+24t^{11})\,\mathrm dt=98[/tex]