7.1 Integration By Parts/36: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
<math>\int_{0}^{\pi}e^{cost}(sin2t)dt</math> = <math>\int_{0}^{\pi}e^{cost}(2sintcost)dt</math> = <math>{-2}\int_{cos0}^{cos\pi}e^{u}{u}du</math> = <math>{-2}{u}e^{u}\bigg|_{cos0}^{cos\pi}-(-2)\int_{cos0}^{cos\pi}e^{u}du</math> = <math>{-2}{u}e^{u}\bigg|_{cos0}^{cos\pi}+{2}e^{u}\bigg|_{cos0}^{cos\pi} du</math> = <math>{2}{u}e^{u}\bigg|_{cos\pi}^{cos0}-{2}e^{u}\bigg|_{cos\pi}^{cos0}du</math> = <math>{2}{cos(0)}e^{cos(0)}-{2}{cos(\pi)}e^{cos(\pi)}-{2}e^{cos(0)}+{2}e^{cos(\pi)}</math> | <math>\int_{0}^{\pi}e^{cost}(sin2t)dt</math> = <math>\int_{0}^{\pi}e^{cost}(2sintcost)dt</math> = <math>{-2}\int_{cos0}^{cos\pi}e^{u}{u}du</math> = <math>{-2}{u}e^{u}\bigg|_{cos0}^{cos\pi}-(-2)\int_{cos0}^{cos\pi}e^{u}du</math> = <math>{-2}{u}e^{u}\bigg|_{cos0}^{cos\pi}+{2}e^{u}\bigg|_{cos0}^{cos\pi} du</math> = <math>{2}{u}e^{u}\bigg|_{cos\pi}^{cos0}-{2}e^{u}\bigg|_{cos\pi}^{cos0}du</math> = <math>{2}{cos(0)}e^{cos(0)}-{2}{cos(\pi)}e^{cos(\pi)}-{2}e^{cos(0)}+{2}e^{cos(\pi)}</math> = <math>{2}(1)e^(1)-{2}(-1)e^(-1)-{2}e^(1)+{2}e^(-1)</math> = <math>{2}e^{1}+{2}e^{-1}-{2}e^{1}+{2}e^{-1}</math> = <math>{2}e^{-1}+{2}e^{-1}</math> = <math>{4}e^{-1}}</math> | ||
<math>{u}</math> = <math> | <math>{u}</math> = <math>{cost}</math> | ||
<math>{du}</math> = <math> | <math>{du}</math> = <math>{-sint}dt</math> | ||
<math>{-du}</math> = <math> | <math>{-du}</math> = <math>{sint}dt</math> | ||
Revision as of 03:03, 23 November 2022
= = = = = = = = = = Failed to parse (syntax error): {\displaystyle {4}e^{-1}}}
=
=
=
= =
= =
