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.

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Area Enclosed by yaxis to Area in Integration