Integration by Parts: Solving x^2(cosx)dx with Step-by-Step Guide

In summary, integration by parts is a mathematical technique used to solve integrals by breaking them down into simpler integrals. It is used when other integration techniques are not applicable and involves choosing parts of the integrand to differentiate and integrate. To perform integration by parts, a function is chosen to differentiate (u) and another to integrate (dv), and then the product rule is used to find their respective derivatives (du and v). The integration by parts formula is ∫udv = uv - ∫vdu, and common mistakes include choosing incorrect functions, incorrect application of the product rule, and not simplifying the resulting integral. Careful attention to these steps is necessary to avoid errors.
  • #1
ldbaseball16
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0

Homework Statement


solve by using intergration by parts x^2(cosx)dx

Homework Equations


My question is i got this answer but my computer algebra system gave me this answer
(x^2-2)sin(x)+2xcos(x) can you tell me where i went wrong??

The Attempt at a Solution


u=X^2
dv=cosx
du=dx
v=sinx

Sx^2(cosx)dx=uv-Svdu=x^2(sinx)-Ssinxdx

S2xcosxdx=2xsinx-(-cosx)+c= final answer= 2xsinx+cosx+C
 
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  • #2
If u=x^2, du=2x*dx. Not du=dx. You have to do integration by parts twice. And why are you integrating 2xcos(x)?
 
  • #3
oo thank you
 

1. What is integration by parts?

Integration by parts is a mathematical technique used to solve integrals by breaking them down into simpler integrals. It is based on the product rule of differentiation and involves choosing parts of the integrand to differentiate and integrate.

2. When is integration by parts used?

Integration by parts is used to solve integrals that cannot be solved using other integration techniques, such as substitution or partial fractions. It is also used to simplify integrals with complicated or multiple terms.

3. How do you perform integration by parts?

To perform integration by parts, you first choose a function to differentiate (u) and another function to integrate (dv). Then, using the product rule, you find du and v. Finally, you substitute these values into the integration by parts formula: ∫udv = uv - ∫vdu.

4. What is the integration by parts formula?

The integration by parts formula is ∫udv = uv - ∫vdu, where u and v are functions of x and du and dv are their respective derivatives.

5. What are some common mistakes when using integration by parts?

Some common mistakes when using integration by parts include choosing the wrong functions for u and dv, forgetting to apply the product rule correctly, and not simplifying the resulting integral. It is important to carefully choose the functions and follow the integration by parts formula step-by-step to avoid errors.

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