Calculus

i need help finding area under curve of:2y=sqrt(3x),y=4, and 2y+1x=4

1. 👍 0
2. 👎 0
3. 👁 168
1. Did you make a sketch?
Your intersectio points are not "nice" making for messy arithmetic.
the curve and y=4 intersect at (64/3 , 4)
the curve and the line x+2y=4 intersect at appr (1.73, 1.14) and the line x+2y=4 intersects y = 4 at ((-4,4)

So you have to find it in two parts:
Left section:
Area = [integral] (4 - (-1/2)x + 2) ) dx from -4 to 1.73
= (4x + (1/4)x^2 - 2x ) dx from -4 to 1.73
= you do the arithmetic

Right section:
Area = Area = [integral] (4 - (1/2)(3x)^(1/2) ) dx from 1.73 to 64/3
= (4x - (1/9)(3x)^(3/2) ) from 1.73 to 64/3
= you do the arithmetic

add up the two parts.

1. 👍 0
2. 👎 0

Similar Questions

1. Calculus 1

The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2, 2)

2. calculus

Notice that the curve given by the parametric equations x=25−t^2 y=t^3−16t is symmetric about the x-axis. (If t gives us the point (x,y),then −t will give (x,−y)). At which x value is the tangent to this curve horizontal?

3. calculus II SURFACE AREA Integration

Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt(1 + 5x) from 1 ≤ x ≤ 7

4. algebra

am I right? 1. Simplify radical expression sqrt 50 5 sqrt ^2*** 2 sqrt ^5 5 sqrt ^10 5 2. Simplify the radical expression sqrt 56x^2 28x 2x sqrt 14*** 2x sqrt 7 sqrt 14x2 3. Simplify the radical expression. sqrt 490y^5w^6 2 sqrt

1. Math:)

A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates

2. Calculus

Consider the curve C parametrized by (x, y) = (cos (5t), sin(−4t)), for −π ≤ t ≤ 2pi How would I go about finding how many times the curve is traversed? Also, how would I find out the radius and center of the circle is? I

3. Calculus

Which of these kinds of problems is not likely to appear on the AP Exam? Finding the zero of a cubic Drawing the graph of an inverse trig function Finding the area of a region in the plane Finding the slope at a point of a curve

4. algebra

A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. Which expresses the ratio of the volume of the candle to its surface area(including the base)? For cone,

1. AP Statistics

A certain density curve looks like an interverted letter V. The first segment goes fro the point (0,0.6) to the point (0.5,1.4). The segment goes from (0.5.1.44) to (1,0.6). (a) Sketch the curve. Verify that the area under the

2. Calculus HELP plz

Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=1 about the -axis. about the x-axis. surface area= ⌠ 2pi * f(x)*sqrt[1 + (f'(x))^2] dx from a to b ⌡ it's been 45 years since I used that

3. Calculus 1

The curve y =|x|/(sqrt(5−x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2,2).

4. Calculus I

Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt(1+5x) from 1