7.1 Integration by Parts

7.1 Integration by Parts - 7.1 Integration by Parts If u...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
7.1 Integration by Parts If u and v are functions of x and have continuous derivatives, then - = du v uv dv u Note: This is the formula for Integration by Parts
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Guidelines for Integration by Parts Try letting dv be the most complicated portion of the integrand that fits a basic integration formula. Then u will be the remaining factor(s) of the integrand. Try letting u be the portion of the integrand whose derivative is a simpler function than u . Then dv will be the remaining factor(s) of the integrand.
Image of page 2
Example 1 Evaluate the integral: - dx x ) ( sin 1 dx x du x u 2 1 1 1 ) ( sin let - = = - Solution: x v dx dv = = ( 29 C x x x C x x x dx x x x x dx x x x x dx x + - + = + - + = - - = - - = - - - - - - 2 1 2 / 1 2 1 2 / 1 2 1 2 1 1 1 ) ( sin 2 1 2 1 ) ( sin ) 1 ( ) ( sin 1 ) ( sin ) ( sin
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example 2- Repeated Application of Integration by Parts Evaluate the integral: - θ θ θ d e ) 2 cos( θ θ θ d du u ) 2 sin( 2 ) 2 cos( let - = = θ θ θ - - - = = e v d e dv - - - - - = θ θ θ θ θ θ θ θ d e e d e ) 2 sin( 2 ) 2 cos( ) 2 cos( θ θ θ d dU ) 2 cos( 4 ) 2sin(2 let U = = θ
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern