(i) First draw the graph of the given curve approximately. To know whether the area bounded by the region is above the x-axis, below the x-axis, left side of y-axis or right side of y-axis.
(ii) Mark the given interval in the figure.
(iii) Then write the appropriate formula
(iv) Need to integrate the function.
(v) Apply the upper and lower limits.
(vi) Put square units for the answer.
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
The area made by the curve above the x-axis will look like the above.
Let y = f(x) be a continuous function defined by the closed interval [a, b]. The area made by the curve below the x-axis will look like the below figure.
Then the area bounded by the curve y = -f(x) is
From those two figures, we can understand that
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
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 that,
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