Question
Find the area of the region bounded by the functions f(x) = x^4 and g(x) = |x|.
a) 1.3
b) 5.2
c) 0.6
d) None of these
a) 1.3
b) 5.2
c) 0.6
d) None of these
Answers
Reiny
Because of the symmetry, we only have to consider the area between
y = x^4 and y = x
They intersect at (0,0) and (1,1)
so the area in quadrant I is
∫ (x - x^4) dx from 0 to 1
= ... trivial from here
remember to double that answer
y = x^4 and y = x
They intersect at (0,0) and (1,1)
so the area in quadrant I is
∫ (x - x^4) dx from 0 to 1
= ... trivial from here
remember to double that answer
oobleck
You ever going to post any of <u>your</u> work?
Using the symmetry of the area,
A = ∫[-1,1] (|x|-x^4) dx = 2∫[0,1] (x-x^4) dx
Using the symmetry of the area,
A = ∫[-1,1] (|x|-x^4) dx = 2∫[0,1] (x-x^4) dx