Area In Integration





In this page area in integration we are going to see the concept how to find area using integration. We have explained this concept with clear steps.

Now let us see area of curves above the x-axis and below x-axis.

Let y = f (x) be a continuous function defined by the closed interval [a,b]. Then the area bounded by the curve y = f (x) is

Area in integration-formula to find the area bounded by y axis

The area made by the curve above the x-axis will look like the below figure.

Let y = f (x) be a continuous function defined by he closed interval [a,b]. Then the area bounded by the curve y =- f (x) is

The area made by the curve below the x-axis will look like the below figure.

From those two figures we can understand if the required area is being above the x-axis then it will be positive. If the required area is being below the x-axis then it will be negative.

Now let us see area of curves which is right side of the y-axis and left side of the y-axis.

Let x = f (y) be a continuous function defined by the closed interval [a,b]. Then the area bounded by the curve x = f (y) is

Formula to find the area bounded by x axis

Let x = - f (y) be a continuous function defined by the closed interval [a,b]. Then the area bounded by the curve x = - f (y) is

If the given curve lies left side of the y-axis with the closed interval [a,b] then area bounded by the region look like

From those two figures we can understand if the required area is being right of the y-axis then it will be positive. If the required area is being left side of the y-axis then it will be negative.

General procedure:

(i) First draw the graph of the given curve approximately. To know whether the area bounded by the region is above the x-axis or below the x-axis.

(ii) Mark the given interval in the figure.

(iii) Then we have to write the appropriate formula

(iv) Need to integrate the function.

(v) Apply the upper and lower limits.

(vi) Put square units for the answer.

      Students can go through the links given below to become master in finding the area bounded by the curves  using integration. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.

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