Table of Contents
Integration by Substitution Class 12th
Integration by substitution is a technique to integrate a function of the form
This can be done by using the substitution rule to transform the function into a simpler form.
The substitution rule states that:
The substitution rule can be used to transform the function into a simpler form. In this example, the function can be transformed into a linear function.
The substitution rule can be used to transform the function into a simpler form. In this example, the function can be transformed into a quadratic function.
The substitution rule can be used to transform the function into a simpler form. In this example, the function can be transformed into a cubic function.
What is Integration?
In mathematics, integration is the process of finding the area under a curve. Integration is one of the fundamental operations of calculus.
Integration Examples
Integration is the mathematical process of finding the area of a curved region by finding the sum of the areas of its many infinitesimal rectangular regions. Let’s look at a couple of integration examples to better understand how this works.
Example 1: Find the area of the region bounded by the curves y = x2 and y = x.
We can think of this region as a series of infinitesimal rectangular regions, as shown below.
To find the area of this region, we will need to find the sum of the areas of all of these rectangles. We can do this by using the formula for the sum of a series:
S = ∑(x i y i )
We can plug in our values for x and y to get:
S = ∑(x i y i )
S = ∑(x2)
S = x3
So, the area of the region is x3.
What should be used for u in the integral?
The symbol u can be used for any variable in an integral.
