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Homework Statement
Can anyone tell me which one is right (LIPET or LIATE)?
Also, in trig, which one come first? sin,cos or tan?
thx
Nope said:1.
Can anyone tell me which one is right (LIPET or LIATE)?
Also, in trig, which one come first? sin,cos or tan?
thx
]
rl.bhat said:Both are correct.
LIPET means Logarithmic, Inverse, Polynomial, Exponential and trigonometric.
LIATE means Logarithmic, Inverse, Algebraic , trigonometric and Exponential.
In the integration by parts , the first two terms usually won't come together. Either one can be taken as u in Intg(u*δv).
Any one of the last two terms can be u, because both are differentiable and integrable.
Integration by parts is a method used in calculus to find the integral of a product of two functions. It is based on the product rule for derivatives, and it allows us to convert a difficult integral into a simpler one that can be solved algebraically.
The acronym LIPET stands for "Logarithmic, Inverse trigonometric, Polynomial, Exponential, and Trigonometric" while LIATE stands for "Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, and Exponential". These are the order of preference for choosing the "u" and "dv" terms in integration by parts. You can use LIPET when the integrand contains a logarithmic or exponential function, and LIATE when it contains an algebraic or trigonometric function.
The formula for integration by parts is ∫udv = uv - ∫vdu, where u and v are the "u" and "dv" terms chosen using LIPET or LIATE. This formula is derived from the product rule for derivatives.
Yes, it is possible to use integration by parts multiple times on the same integral. This is known as repeated integration by parts. However, it may not always lead to a simpler integral, so it is important to carefully choose the "u" and "dv" terms each time.
Yes, there are several other techniques for finding integrals, such as substitution, trigonometric substitution, partial fractions, and integration by trigonometric identities. It is important to be familiar with all of these techniques and know when to use them in order to solve integrals effectively.