Area Enclosed by yaxis

In this page area enclosed by yaxis we are going to see some example problems to know how to find area bounded by region and y-axis.


Area enclosed by yaxis: Examples

Example 1:

Find the area bounded by the curve y = 2x + 1, y = 3, y = 5 and y-axis.

Solution:

First let us draw the rough graph for the given line. For that we need to find x and y intercepts.

x-intercept :                                    y-intercept :

put y = 0                                         put x = 0

0 = 2x + 1                                        y = 2 (0) + 1

2x + 1 = 0                                        y = 0 + 1

     2x = -1                                       y = 1

      x = -1/2

      x = - 0.5

So we got two points (-0.5, 0) and (0, 1)


The required area is right side of the y-axis. So we need to use the following formula.

Now we need to change this equation in terms of y

  y = 2x + 1

  2x = y - 1

   x = (y-1)/2


Example 2:

Find the area bounded by the curve y = 2x + 4, y = 1, y = 3 and y-axis.

Solution:

First let us draw the rough graph for the given line. For that we need to find x and y intercepts.

x-intercept :                                    y-intercept :

put y = 0                                         put x = 0

0 = 2x + 4                                        y = 2 (0) + 4

2x + 4 = 0                                        y = 0 + 4

     2x = -4                                       y = 4

      x = -4/2

      x = - 2

So we got two points (-2, 0) and (0, 4)


The required area is left side of the y-axis. So we need to use the following formula.

Now we need to change this equation in terms of y

  y = 2x + 4

  2x = y - 4

   x = (y-4)/2

  -x = (4-y)/2

Note:

  • In these type of problems,  graph is very important to find out the limits.
  • Without the graph to determine which function is the upper one and which one is the lower one, is difficult.
  • Area between two curves is always positive. If we get negative answer then we will come to know that we had done some mistake and we can correct it.

      Students can go through the problem, and try to solve it on their own, in the same way we had discussed above. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.

HTML Comment Box is loading comments...




Properties




Area Enclosed by yaxis to Area in Integration
Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.

Recent Articles

  1. Twin Prime Numbers

    Mar 24, 23 05:25 AM

    Twin Prime Numbers

    Read More

  2. Twin Prime Numbers Worksheet

    Mar 24, 23 05:23 AM

    tutoring.png
    Twin Prime Numbers Worksheet

    Read More

  3. Times Table Shortcuts

    Mar 22, 23 09:38 PM

    multiplicationtricks3.png
    Times Table Shortcuts - Concept - Examples

    Read More