About Integration of UV Formula
Integration of the product of the two functions u and v is easily calculated using the uv formula. Additionally, the two functions employed in this uv formula integration can be algebraic expressions, trigonometric ratios, or logarithmic functions. We express the supplied integral in terms of a known integral by expanding the differential of a product of functions. As a result, uv formula integration is often referred to as integration by parts or the product rule of integration.
What do you mean by Integration of UV Formula?
- The uv formula integration is a specific rule of parts integration. We've combined the output of two functions here. If the two functions u(x) and v(x) are of the form ∫u dv, then the Integration of uv formula is:
- ∫ uv dx = u ∫ v dx - ∫(u' ∫ v dx) dx
- ∫ u dv = uv - ∫v du
- Here, u is a function of u(x)
- dv is a variable dv
- v is a function of v(x)
- du is a variable du
Integration of UV Formula
- To get the integral of the product of two functions, we use the simple techniques below: Identify the u(x) and v functions (x). u(x) is chosen using the ILATE rule: whatever comes first in this order: A function that is inverse, logarithmic, algebraic, trigonometric, or exponential.
- Find derivative of u: du/dx
- Integrate v: ∫v dx
- Fill in the formula's values. ∫ u.v dx = u.∫ v dx - ∫(∫v.dx u'). dx
Integration of UV Formula Derivation
??????? Using the product rule of differentiation, we shall get the uv formula integration. Consider the two functions u and v, where y = uv. When we apply the product differentiation rule, we get:
- d/dx (uv) = u(dv/dx) + v(du/dx)
We've rearranged the terms.
- u(dv/dx) = d/dx(uv) - v(du/dx)
With regard to x, integrate on both sides.
- ∫ u(dv/dx) (dx) = ∫d/dx (uv) dx - ∫v (du/dx)dx
⇒ ∫u dv = uv - ∫v du
Hence, the integration of uv formula is derived.
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