trig_substitution - Sec0on8.3 Integralsinvolving 2 x 2 a a...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Trigonometric Subs0tu0on Sec0on 8.3
Image of page 1

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

View Full Document Right Arrow Icon
a 2 x 2 = a cos( θ ) Subs0tu0on: Back‐subs0tu0on: θ = sin 1 ( x / a ) sin( θ ) = x a cos( θ ) = a 2 x 2 a x = a sin( θ ) dx = a cos( θ ) d θ a 2 x 2 = a cos( θ ) Integrals involving a 2 x 2 x = a sin( θ ) a θ a θ x
Image of page 2
a 2 + x 2 Subs0tu0on: Back‐subs0tu0on: θ = tan 1 ( x / a ) sin( θ ) = x a 2 + x 2 cos( θ ) = a a 2 + x 2 x = a tan( θ ) dx = a sec 2 ( θ ) d θ a 2 + x 2 = a sec( θ ) Integrals involving a 2 + x 2 a = a 2 + x 2 cos( θ ) x = a tan( θ ) θ a θ x
Image of page 3

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

View Full Document Right Arrow Icon
Subs0tu0on: Back‐subs0tu0on: θ = sec 1 ( x / a ) sec(
Image of page 4
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