Question

Evaluate ModifyingBelow Integral from nothing to nothing With Upper C xy dx plus (x plus y )dy along the curve y equals 2 x squared from (1 comma 2 )to (2 comma 8 ).

Answer 1

`y=2x^2\implies\mathrm dy=4x\,\mathrm dx`

Then in the integral we have

`\displaystyle\int_Cxy\,\mathrm dx+(x+y)\,\mathrm dy=\int_1^2(2x^3+4x(x+2x^2))\,\mathrm dx=\int_1^210x^3+4x^2\,\mathrm dx=\boxed{\frac{281}6}`