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Differentiate the product uvuvuv with respect to xxx.

A

It is obtained by integrating and rearranging the product rule.

B

For x>0x>0x>0, ∫ln⁡x dx=xln⁡x−x+C\boxed{\displaystyle \int \ln x\,dx=x\ln x-x+C}∫lnxdx=xlnx−x+C​.

C

For definite integrals, integration by parts becomes ∫abudvdx dx=[uv]ab−∫abvdudx dx\boxed{\displaystyle \int_a^b u\frac{dv}{dx}\,dx=[uv]_a^b-\int_a^b v\frac{du}{dx}\,dx}∫ab​udxdv​dx=[uv]ab​−∫ab​vdxdu​dx​.

D

ddx(uv)=udvdx+vdudx\displaystyle \frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}dxd​(uv)=udxdv​+vdxdu​

Card 1 of 22

1.9.29 Integration by parts (A-level only) Flashcards

  1. A Level
  2. /Maths
  3. /1.9.29 Integration by parts (A-level only)

22 flashcards on OCR (MEI) A Level Maths 1.9.29 Integration by parts (A-level only): the key formulae, methods and definitions you need to recall for Component 01, Component 02 and Component 03.

Flashcards