Integration by parts formula
∫udv= uv-∫vdu
The integration by parts formula is a technique used in calculus to integrate the product of two functions. It is often written in the following form:
∫u dv = uv – ∫v du
where ∫u dv represents the integral of the product of the functions u and dv, uv is the product of the functions u and v, ∫v du represents the integral of the product of the functions v and du.
The formula can also be expressed in terms of differential notation as:
d(uv) = u dv + v du
Rearranging this equation we get:
∫u dv = uv – ∫v du
This formula is particularly useful when one of the functions in the integral is easily integrable, but the other is not. In this case, we can choose which function to be u and which to be dv based on ease of integration. We then use the formula to transform the integral to a form that is easier to solve.
More Answers:
Discover The Pythagorean Identity: Sin^2X + Cos^2X = 1Mastering Trigonometric Identities: Simplifying Expressions Using 1 + Tan^2X = Sec^2X Identity
Proving 1 + Tan^2X = Sec^2X Using Trigonometric Identity