Applications of Definite Integrals

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Let y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given byLet y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given by

(ii) The area bounded by the curve x = f (y)

y = axis and the abscissae at y = c and y = d is given by

Note 1:

The area bounded by the curves f(x) and g(x) and the ordinates x = a and x = b is given by

Note 2:

If curve f (x) lies above the x-axis and g (x) lies below the x-axis then area bounded by f (x) and g (x) is

Note 3:

If f (a) and f (b) are opposite in sign then the curve crosses the x-axis say at c.

Then the area bounded the curve f (x), x-axis and the ordinates x = a and x = b is

Example:

Find the area of the region between the X-axis and the graph of f(x) = x³ - x² - 2x   -1 ≤ x < 2.

Solution:

Let us find the values of x in the given interval, for which

f(x) = 0

x³ - x² - 2x = 0

x(x² - x - 2) = 0

Partition the domain [-1, 2] to subintervals [-1, 0] and [0, 2]