Question 2: What is the product rule of integration?Īnswer: The Product Rule of integration allows us to integrate the product of two functions. Question 1: What are integration and differentiation?Īnswer: Differentiation refers to the act of finding the rate of change of the gradient/slope of any function whereas integration refers to the area under the curve of function with regards to the x-axis. Question 1: Find ∫ e x (sin x + cos x) dxĪnswer :f ’(x) = df(x)/dx = d sin x / dx = cos x. ∫ dx = e x (x – 1) / (x + 1) + C More Solved Examples for You Hence, the integrand is of the form: e x. (Source: blue diamond) Integration Rules – Example 1įind ∫ e x ] dx Let’s look at an example to understand it well. I = e x f(x) – ∫ e x f ’(x) dx + ∫ e x f ’(x) dx + C = e x f(x) + C Substituting the value of I1 in equation (1), we get Let the first function = f 1(x) = f(x) and the second function = g 1(x) = e x. To solve I 1, we will use integration by parts. I = ∫ e x f(x) dx + ∫ e x f ’(x) dx = I 1 + ∫ e x f ’(x) dx … (1)
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |