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The area of the region bounded by the curve y = f (x) the ordinates x = a and x = b.

Now we calculate the sum of all these rectangles, which are of negligible width, we get the required area.

Area of the required region = Sum of the areas of the Infinitesimal rectangles

Area of the required region = âˆ«_{a}^{b} dA

dA = dx.y where dx = Width of the rectangle.

y = Height of the rectangle.

Given curve y = f(x)

â‡’ Area of the required region = âˆ«_{a}^{b} y dx = âˆ«_{a}^{b} f(x)dx

Area under the curve = âˆ«_{c}^{d} g(y)dy

In this case, the limits of the integral are determined between the lines - y = c, and y = d.

So, the area under the curve is given by integral of g(y) dy from c to d.

The area of the region between the curve and the X-axis, we split the figure into two parts,

Here, the value of the function is positive above the X-axis and negative below the X-axis.

Toatal area under the curve = A_{1} + |A_{2}|

The area of the region bounded by the curve y = f (x) the ordinates x = a and x = b.

Now we calculate the sum of all these rectangles, which are of negligible width, we get the required area.

Area of the required region = Sum of the areas of the Infinitesimal rectangles

Area of the required region = âˆ«_{a}^{b} dA

dA = dx.y where dx = Width of the rectangle.

y = Height of the rectangle.

Given curve y = f(x)

â‡’ Area of the required region = âˆ«_{a}^{b} y dx = âˆ«_{a}^{b} f(x)dx

Area under the curve = âˆ«_{c}^{d} g(y)dy

In this case, the limits of the integral are determined between the lines - y = c, and y = d.

So, the area under the curve is given by integral of g(y) dy from c to d.

The area of the region between the curve and the X-axis, we split the figure into two parts,

Here, the value of the function is positive above the X-axis and negative below the X-axis.

Toatal area under the curve = A_{1} + |A_{2}|