Calculus I integral problem If
evaluate

In terms of typing this in on a keyboard, you could say -sqrt(35)/2

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Work Shown:

We'll use u-substitution here

Let u = x^2, so du/dx = 2x which rearranges to du = 2x*dx and we can say xdx = du/2

Because we are changing from x^2 to u, this means we need to change the limits of integration

If x = -2, then u = x^2 = (-2)^2 = 4

If x = 0, then u = x^2 = 0^2 = 0

Despite 4 being larger than 0, we still place 4 at the bottom limit and we'll just swap them later.

This means we have the following steps

Notice when I swapped the limits of integration (4 and 0 to 0 and 4) I placed a negative sign out front.

The rule is

i just took the test, the correct answer is .. 31.5 in.