Homework Help: Calculus

Posted by Alex on Thursday, April 12, 2012 at 10:32pm.

Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.
Between y = −x and y = x/2 for x in [0, 6]

Calculus - Reiny, Thursday, April 12, 2012 at 11:31pm
Did you follow suggestion and sketch the lines?
I see a triangle with vertices
(0,0), (6,3) and (6,-6)

You certainly would not need Calculus for this
base = 9, height = 6
area = (1/2)(9)(6) = 27

If you have to use Calculus ....
effective height = x/2 - (-x) = (3/2)x
area = ∫(3/2) x dx from 0 to 6
= (3/4)x^2 | from 0 to 6
= (3/4)(36) - 0 = 27

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