Marlena B.

asked • 11/19/17

Draw a graph of the signed area represented by the integral and compute it using geometry.

∫10−10|x|dx∫−1010|x|dx =

1 Expert Answer


Kenneth S. answered • 11/19/17

Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018

Marlena B.

Yes it is.


Kenneth S.

I think that this must be a definite integral with lower limit -10 and the upper limit 10, and the integrand is simply |x|.
The integrand function is V-shaped passing through the origin and it's the line y=x in the first quadrant, and the line y = -x in the second quadrant. Therefore the definite integral is two times the area of the triangle in the first quadrant bounded above by y=x and below by the x-axis.
This triangle's area is ½•102 and so the definite integral from -10 to 10 of |x| must be 100 sq units.


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