$\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

where D is the triangule region with C as its boundary, given by the set

$D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}$

So we have

$\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx$

$\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}$

5 0

3 years ago

micaela had $22 to spend on seven notebooks. After buying them she had $1. How much did each notebook cost?

My name is Ann [436]

$22-$1= $21
$21/7 = $3 per notebook

4 0

2 years ago

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