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The area of the region enclosed between two curves.

Consider two curves f (x) and g(x).

The end points on both sides of the region, which can be found by solving the equations of

curves. These points be (x_{1}, y_{1}) and (x_{2}, y_{2}).

The area of the region can be found by using the formula = âˆ«_{x1}^{x2} y . dx

Here, y is the height of the strip y =f(x) - g(x)

If f(x) â‰¥ g(x):y = f(x) - g(x) And If f(x) â‰¤ g(x):y = g(x) - f(x)

Area of the region = âˆ«_{x1}^{x2} [f(x) - g(x)] . dx

Area of the region = âˆ«_{x1}^{x2} f(x) dx - âˆ«_{x1}^{x2} g(x) dx

Now another case the area of the region enclosed between these two curves.

Consider two curves f (x) and g(x).

We divide the region into two parts, and write the integral.

Area of the region = âˆ«_{x1}^{x2} [f(x) - g(x)] dx - âˆ«_{x1}^{x2} [g(x) - f(x)] dx

The area of the region enclosed between two curves.

Consider two curves f (x) and g(x).

The end points on both sides of the region, which can be found by solving the equations of

curves. These points be (x_{1}, y_{1}) and (x_{2}, y_{2}).

The area of the region can be found by using the formula = âˆ«_{x1}^{x2} y . dx

Here, y is the height of the strip y =f(x) - g(x)

If f(x) â‰¥ g(x):y = f(x) - g(x) And If f(x) â‰¤ g(x):y = g(x) - f(x)

Area of the region = âˆ«_{x1}^{x2} [f(x) - g(x)] . dx

Area of the region = âˆ«_{x1}^{x2} f(x) dx - âˆ«_{x1}^{x2} g(x) dx

Now another case the area of the region enclosed between these two curves.

Consider two curves f (x) and g(x).

We divide the region into two parts, and write the integral.

Area of the region = âˆ«_{x1}^{x2} [f(x) - g(x)] dx - âˆ«_{x1}^{x2} [g(x) - f(x)] dx