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The graph of y = x³ and the line y = 16x enclose two… | StemPy Lab
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The graph of y = x³ and the line y = 16x enclose two regions, as in the figure. What is the total area of the two regions?
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High School (11–12)
Functions and Calculus › Application of Integrals
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The graph of
y
=
x
3
y = x^3
y
=
x
3
and the line
y
=
16
x
y = 16x
y
=
16
x
enclose two regions, as in the figure. What is the total area of the two regions?
Fig. 1: The graph of y = x cubed, in blue, and the line y = 16x, in orange. They cross at three points, x = -4, 0 and 4. The two enclosed regions are shaded, the right one in orange and the left one in green.
0
0
0
64
64
64
128
128
128
256
256
256
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← The figure shows y = eˣ and y = e⁻ˣ from x = 0 to the dashed line x = 1. The curves start together at (0, 1). What is the area of the shaded region, to two decimal places?
The parabolas x = y² and x = 2 - y² enclose the shaded region in the figure. What is its area? →
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Functions and Calculus › Application of Integrals
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