Find integral top=8 bottom=0 f(x)dx if f(x) = 6 for x < 6, x for x ≥ 6.
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6 . . . . . . 8
∫ 6 dx + . ∫ x dx =
0 . . . . . .6
6x from 0 to 6 and (x^2 / 2) from 6 to 8
(36 - 0) + (32 - 18) = 36 + 14 = 50 <---------- Answer
Thought: This is easily done with Plane Geometry.
You have a 6 by 6 square for 36 and a trapezoid (on its side) averaging ((6 + 8) / 2) = 7 in height and with a width of 2 and thus an area of 2 * 7 = 14.
And again 36 + 14 = 50.
I guess you could call that a check:)
.
∫ 6 dx + . ∫ x dx =
0 . . . . . .6
6x from 0 to 6 and (x^2 / 2) from 6 to 8
(36 - 0) + (32 - 18) = 36 + 14 = 50 <---------- Answer
Thought: This is easily done with Plane Geometry.
You have a 6 by 6 square for 36 and a trapezoid (on its side) averaging ((6 + 8) / 2) = 7 in height and with a width of 2 and thus an area of 2 * 7 = 14.
And again 36 + 14 = 50.
I guess you could call that a check:)
.