Help with integrals?

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1 Answer
Feb 8, 2018

I'll answer the first question and leave the other question to another contributor.

The absolute value function, #y = |x|#, appears as follows:

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We know that a definite integral is pretty much an area, so we want to calculate the area between the x-axis and the graph on the interval #[-1, 1]#. We can see that this is two right triangles of length and height #1#, thus the area is

#A = (1 * 1)/2 + (1 * 1)/2 = 1/2 + 1/2 = 1# square unit

We can also use calculus, but I don't think it's necessary for this problem.

Hopefully this helps!