Interesting that only integrals along the $x$ -axis are suggested when integrating along the $y$ -axis would be much simpler... Anyway, you have to split the interval of integration into two. The "height" of the region is not uniform over the entire interval.

When $y=0$ , we have $0^2=x-1\implies x=1$ . When $y=2$ , we have $2^2=x-1\implies x=5$ . Then the area we want is given by

$\displaystyle\int_0^12\,\mathrm dx+\int_1^52-\sqrt{x-1}\,\mathrm dx$

which seems to agree with the last option.

5 0

3 years ago

Hi! how do i do this?

lapo4ka [179]

Answer:

p = 2

Step-by-step explanation:

A rational function has a vertical asymptote where the denominator is zero.

Your function will have a denominator that is zero when ...

x -p = 0 ⇒ x = p

We are told there is a vertical asymptote at x = 2. That means ...

p = 2

4 0

2 years ago

Building A is 880 ft tall and contains 71 stories. Building B contains 100 stories If the two buildings have the same number of

Marta_Voda [28]

R. a = 2, b = 4. s. A = 13°, c = 11. t. b = 40, c = 80. 2. The length of a path going ... A staircase is to rise 10 feet 8 inches in a horizontal distance of 13 feet 4 inches. ... From a balloon directly above a certain building, the angle of depression of a river ... Find the approximate height of the kite above level ground if 85 meters

4 0

3 years ago

Let the domain and codomain of functions f and g be the set of integers, f(x) = 2x+3, g(x) = 3x+2 What is the composition of f a

shutvik [7]

Answer:

Composition of f and g = 6x + 7

Composition of g and f = 6x + 11

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 3x + 2

f(g(x)) = 2(g(x)) + 3 = 2(3x + 2) + 3 = 6x + 4 + 3 = 6x + 7

g(f(x)) = 3(f(x)) + 2 = 3(2x + 3) + 2 = 6x + 9 + 2 = 6x + 11

5 0

3 years ago