Notes On Area Between Simple Curves - CBSE Class 12 Maths

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 (x1, y1) and (x2, y2).

The area of the region can be found by using the formula =x1x2 y . dx

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

If f(x) ≥ g(x):y = f(x) - g(x) And If f(x) ≤ g(x):y = g(x) - f(x)

Area of the region = x1x2 [f(x) - g(x)] . dx

Area of the region = x1x2 f(x)  dx - ∫x1x2 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 = x1x2 [f(x) - g(x)]  dx - ∫x1x2 [g(x) - f(x)] dx

Summary

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 (x1, y1) and (x2, y2).

The area of the region can be found by using the formula =x1x2 y . dx

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

If f(x) ≥ g(x):y = f(x) - g(x) And If f(x) ≤ g(x):y = g(x) - f(x)

Area of the region = x1x2 [f(x) - g(x)] . dx

Area of the region = x1x2 f(x)  dx - ∫x1x2 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 = x1x2 [f(x) - g(x)]  dx - ∫x1x2 [g(x) - f(x)] dx

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