Evaluate the line integral ? cx2zds, where c is the line segment from (0,5,2) to (2,7,8).

We want to evaluate the line integral: x^2*zds on the line segment that goes from (0,5,2) to (2,7,8), we will get that the line integral is equal to 24.

So we just need to solve a triple integral, notice that we don't have a dependence on y, then we write the points just as (0, 2) and (2, 8)

Then we can find a linear relation between x and z, such that the slope of that line is:

And when x = 0, we have z = 2.

Then the linear equation is:

z = 3*x + 2

Then the line integral is just:

Where the second integral is just equal to 2, so we have:

If you want to learn more, you can read:

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step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

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step-by-step explanation: