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gladu [14]
2 years ago
6

1. Find the area of the finite region enclosed by the curve y=2√x and the lines x=3 and x=0.

Mathematics
2 answers:
larisa86 [58]2 years ago
7 0

9514 1404 393

Answer:

  1. 4√3 ≈ 6.92820
  2. 10

Step-by-step explanation:

1. The integral from 0 to 3 of 2x^(1/2) can be found using the power rule:

  area = 2(2/3x^(3/2)) for x = 3

  = 4/3(3√3)

  area = 4√3 . . . square units

__

2. The line equation for y=0 is corrupted, so we assume the line equation for x is intended to be x=0. The area is a right triangle with side lengths 4 and 5, so the geometric area formula applies:

  A = 1/2bh = 1/2(4)(5) = 10

The area of the triangular region is 10 square units.

_____

<em>Additional comment</em>

If you really intend the right bound of the enclosed area to be x=b, then the area is the shape of a trapezoid. One base length is 5; the other is (5 -5/4b), and the height of the trapezoid is (b). The area is then ...

  A = 1/2(b1+b2)h

  A = 1/2(5 +5 -5/4b)(b) = 5b -5/8b^2

anygoal [31]2 years ago
5 0

Answer:

wow this is hard, I am not really sure.

Step-by-step explanation:

SORRY! :(

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