Question

Calculate the area, in square units, of the region bounded by the line x=2 on the left, the curve f(x)=ln(x-6)+1 on the right, the line y=3 above, and the x-axis below. Give an exact answer, in terms of e.

Answer #1

1- Find the area enclosed by the given curves.
Find the area of the region in the first quadrant bounded on the
left by the y-axis, below by the line above left
by y = x + 4, and above right by y = - x 2 + 10.
2- Find the area enclosed by the given curves.
Find the area of the "triangular" region in the first quadrant that
is bounded above by the curve , below by the curve y...

Find the area of the region in the ?? x y -plane bounded above
by the graph of the function ?(?)=9 , below by the ? -axis, on the
left by the line ?=8 , and on the right by the line ?=19 . The area
is

Find the area of the region bounded by the y-axis, the curve y =
ln(x+ 1),
and the tangent line to y = ln(x + 1) at x = 3.

(1 point) Find the area of the region in the ??-plane bounded
above by the graph of the function f(x)=9, below by the ?x-axis, on
the left by the line ?=2, and on the right by the line ?=15.

Estimate the area of the region bounded between the curve f(x) =
1 x+1 and the horizontal axis over the interval [1, 5] using a
right Riemann sum. Use n = 4 rectangles first, then repeat using n
= 8 rectangles. The exact area under the curve over [1, 5] is ln(3)
≈ 1.0986. Which of your estimates is closer to the true value?

Find the area of the "triangular" region in the first quadrant that
is bounded above by the curve y=e^3x, below by the curve y=e^2x,
and on the right by the line x=ln2

Use integrals to calculate the area of the region bounded by x=2
on the left and the function x^2+y^2=25 on the right.

Use the midpoint rule with 4 rectangles to approximate the area
of the region bounded above by y=sinx, below by the ?x-axis, on
the left by x=0, and on the right by ?=?

Calculate the total area of the region described. Do not count
area beneath the x-axis as negative. Bounded by the curve y = 7
square root x
, the x-axis, and the lines x = 0 and x = 16

Consider a lamina of density ρ = 1 the region bounded by the
x-axis, the
y-axis, the line x = 5, and the curve y = e^x.
Find the centroid ( ̄x, ̄y). (Simplify, but
leave your answer as an exact expression not involving
integrals.)

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