How do you evaluate this integral? step by step plz
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How do you evaluate this integral? step by step plz

[From: ] [author: ] [Date: 11-12-08] [Hit: ]
we know that |x| = x.So the whole thing becomes ∫(-3,3) 7dx - 2∫(0,∫x = .= 33.Hope this is helpful.......
∫(7-|x|)dx
****Note it has limits from [-3,3]
I'm not looking the collection of antiderivatices with constant C, i'm looking for the Area beneath that function on top of x axis from[-3,3]

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So we can split the integral into ∫7 - ∫|x|

Then since |x| is an even function (that is, it is symmetric about the x-axis) and the limits of integration are symmetric, we can say ∫(-3,3) |x| dx = 2∫(0,3) |x| dx

But on the interval (0,3), we know that |x| = x.

So the whole thing becomes ∫(-3,3) 7dx - 2∫(0,3) xdx

But these are just power rules:
∫7 = 7x
∫x = .5x^2

Then plugging in the limits gives

= (7*3-7*(-3)) - 2(1/2)(3^2 - 0^2)

= (42) - (1)(9)

= 33.

Hope this is helpful.
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