Integration by Parts: What's the Sign of that Last Term?

In summary, The integration by parts formula is derived from the formula for the product of derivatives, d(u * v) = u * dv + v * du. To use the formula, integrate both sides and subtract int(v * du). It's important to remember this formula in math.
  • #1
tandoorichicken
245
0
I forgot a little detail in the integration by parts formula
Is it [itex]\int u \,dv = uv[/itex] + or - [itex]\int v \,du[/itex]
I don't remember if its plus or minus...
 
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  • #2
Just remember that the integration by parts formula is deriviable from the formula for the product of a deriviatives.

d(u * v) = u * dv + v * du.

Now integrate both sides subtract int(v *du). Isn't math woinderful :-)
 
  • #3
Just remember that the integration by parts formula is deriviable from the formula for the product of a deriviatives.

d(u * v) = u * dv + v * du.

Now integrate both sides subtract int(v *du). Isn't math woinderful :-)
 

Related to Integration by Parts: What's the Sign of that Last Term?

1. What is Integration by Parts?

Integration by Parts is a mathematical technique used to find the integral of a product of two functions. It is based on the product rule of differentiation and involves choosing which function to differentiate and which function to integrate.

2. Why is Integration by Parts useful?

Integration by Parts is useful in evaluating integrals that cannot be solved by other methods such as substitution or partial fractions. It allows us to simplify complex integrals and express them in terms of simpler integrals.

3. How do you know which function to differentiate and which to integrate?

The choice of which function to differentiate and which to integrate is usually made based on the LIPET rule, which stands for Logarithmic, Inverse trigonometric, Polynomial, Exponential, and Trigonometric functions. In general, the function that is easier to integrate should be chosen for integration.

4. What is the sign of the last term in Integration by Parts?

The sign of the last term in Integration by Parts depends on the sign of the derivative of the function being integrated. If the derivative is positive, the last term will be positive. If the derivative is negative, the last term will be negative.

5. Can Integration by Parts be used to solve definite integrals?

Yes, Integration by Parts can be used to solve definite integrals by applying the limits of integration to the final integral expression. This allows us to find the exact value of the definite integral.

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