# mathematics

find the area of the region between the curve y = 3-x^2 and the line y = -1 by integrating with respect to y

you first have to solve for x
x=(3-y)^(1/2)
then area

⌠ (3-y)^(1/2 dy from -1 to 3

=-2/3 (3-y)^(3/2 | from -1 to 3
= -2/3(0 - 8)
= 16/3

but this is only half the region, so the area = 32/3 units^2

Question: Why would anybody ask you to do a question the hard way, the other way with respect to x is easier.

1. 👍 0
2. 👎 0
3. 👁 132
asked by denisa

## Similar Questions

1. ### Calculus

There is a graph of y=1/sqrtx.Show that the area of the region between line and curve at x=1 and x=3 is 3-(5sqrt3/3). 👍 1 👎 1 👁 33 asked by Raj yesterday at 6:35am "Show that the area of the region between line and curve"

asked by Raj on December 19, 2019
2. ### Calculus

Find the area above curve y=(1/2*x-2)^6+5 enclosed by a line cutting at (0,y) and (x,y). Note.It is a straight line. Huh? It seems that you want the area under some arbitrary horizontal line. So, let's say the line is through

asked by Raj on December 25, 2019
3. ### Calculus

Find the area above curve y=(1/2*x-2)^6+5 enclosed by a line cutting at (0,y) and (x,y). Note.It is a straight line. 👍 0 👎 0 👁 85 asked by Raj Dec 22, 2019 Huh? It seems that you want the area under some arbitrary

asked by Raj on December 25, 2019
4. ### Math

The line has equation y=2x+c and a curve has equation y=8-2x-x^2. 1) for the case where the line is a tangent to the curve, find the value of the constant c. 2) For the case where c = 11, find the x-coordinates of the points of

asked by Confused by Math on September 20, 2016
5. ### Calculus

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where

asked by Jessy152 on February 27, 2013
6. ### calculus

Find the volume of the solid generated by revolving the region about the given line. The region is in the first quadrant bounded above by the line y= sqrt 2, below by the curve y=secxtanx, and on the left by the y-axis. Rotate the

asked by ashley on May 23, 2011
7. ### calculus

A region is bounded in the second quadrant by the curve y = ln(1–x), the line y=3, and the y-axis. Find the area of the region.

asked by bex on May 22, 2014
8. ### calculus

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

asked by Bree on May 20, 2016
9. ### calculus

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b > 0. Find the value of b so that the area of the region R is 288 square units.

asked by Anonymous on August 29, 2015
10. ### calculus

Find the volume of the solid generated by revolving the region about the given line. The region in the second quadrant bounded above by the curve y = 16 - x2, below by the x-axis, and on the right by the y-axis, about the line x =

asked by Tiffany on April 12, 2013
11. ### Calculus AB: Area Between Curves

Hello! I'm having trouble understanding how I'm supposed to work out this problem. Any help would be appreciated! Find the area of the region bounded by the curve y = f(x) = x3 – 4x + 1 and the tangent line to the curve y = f(x)

asked by Pax on March 18, 2015

More Similar Questions