1. Find the area of the finite region enclosed by the curve y=2√x and the lines x=3 and x=0.
2 answers:
9514 1404 393
Answer:
- 4√3 ≈ 6.92820
- 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
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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.
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<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
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Answer:
<em>The shaded region has an area of 1400 square units</em>
Step-by-step explanation:
<u>Area of Compound Shapes</u>
We are given a shape and it's required to calculate its area. The shape can be divided into three rectangles as shown in the figure attached below.
The lengths of these rectangles are x, y, and z.
The value of x can be calculated as:
x = 60 - 15 - 10 = 35
Similarly:
y = 60 - 15 = 45
z = y = 45
The first rectangle has dimensions of x by 10, thus its area is:
A1 = 35*10 = 350
The second rectangle has dimensions of 60 by 10:
A2 = 60*10 = 600
The third rectangle has dimensions y by 10:
A3 = 55*10 = 450
The shaded area is:
A = 350 + 600 + 450 = 1400
The shaded region has an area of 1400 square units
