# Quick help with line integrals

## Homework Statement

$$\int_{C}(x+yz)dx + 2xdy + xyzdz$$

C goes from (1,0,1) to (2,3,1) and (2,3,1) to (2,5,2)

## The Attempt at a Solution

For C going from (1,0,1) to (2,3,1)
$$x=1+t, y=3t, z=1; 0\leq t \leq 1$$
$$x'(t)=1, y'(t)=3, z'(t)=0$$

$$\int^{1}_{0}(1+t+3t)*1dt + 2(1+t)*3dt + 0$$
$$=\int^{1}_{0}1+4t+6+6tdt$$
$$[7t+5t^{2}]^{1}_{0}=12$$

For C going from (2,3,1) to (2,5,2)
$$x=2, y=1+2t, z=t; 1\leq t \leq 2$$
$$x'(t)=0, y'(t)=2, z'(t)=1$$

$$\int^{2}_{1}0 + 2*2*2dt + 2(1+2t)tdt$$
$$=\int^{2}_{1}8+2t+4t^{2}dt$$
$$[8t+t^{2}+\frac{4}{3}t^{3}]^{2}_{1}=\frac{55}{3}$$

Total C is $$12+\frac{55}{3} = \frac{91}{3}$$
However, the answer in the book says 97/3, so I'm not sure what I did wrong

## Answers and Replies

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