How to find the area under the curve y=2x+4 from x=0 to x=2 ?

1 Answer
Jim H · Truong-Son N.
Aug 22, 2015

Either find #int_0^2 (2x+4) dx# or use geometry.

Explanation:

Using the integral, we evaluate:

#int_0^2 (2x+4) dx#

Using the Fundamental theorem of Calculus, we get:

#int_0^2 (2x+4) dx = (x^2+4x)]_0^2#

# = [(2)^2+4(2)] - [(0)^2+4(0)]#

# = 12#

Without the integral, we could note that the region is a rectangle with base 2 and height 4, topped by a triangle with base 2 and height 4, so the total area is:

#(2)(4) + (1/2(2)(4)) = 8 + 4 = 12#

Here is a picture of the region:

graph{(y-2x-4)sqrt(2x-x^2)(y) <= 0 [-5, 5, -1, 10]}

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