The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.
Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is
π (radius) (height) = π (1/y)² ∆y = π/y² ∆y
and the volume of a stack of n such disks is
where 
is a point sampled from the interval [1, 5].
As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,
Explanation:
The line of reflection is the perpendicular bisector of the segment joining a point with its reflected image.
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The segment joining a point with its reflection is as short as possible consistent with the requirement that the reflected point be the same distance from the line that the original is. That means it is perpendicular to the line of reflection. Since the distance from that line is the same on either side, the line of reflection bisects the joining segment.
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 2 and c = - 2 , then
y = - 2x - 2 ← is the equation of the line
To find the x- intercept let y = 0 in the equation and solve for x , that is
- 2x - 2 = 0 ( add 2 to both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
The x- intercept is - 1 → B
Answer:
In Section 6.1, we introduced the logarithmic functions as inverses of exponential functions and
discussed a few of their functional properties from that perspective. In this section, we explore
the algebraic properties of logarithms. Historically, these have played a huge role in the scientific
development of our society since, among other things, they were used to develop analog computing
devices called slide rules which enabled scientists and engineers to perform accurate calculations
leading to such things as space travel and the moon landing. As we shall see shortly, logs inherit
analogs of all of the properties of exponents you learned in Elementary and Intermediate Algebra.
We first extract two properties from Theorem 6.2 to remind us of the definition of a logarithm as
the inverse of an exponential function.
Step-by-step explanation:
Hope this helps
