7.1 Integration By Parts/32: Difference between revisions
No edit summary |
No edit summary |
||
| Line 13: | Line 13: | ||
<math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg|_0^t</math><br> | <math>\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg|_0^t</math><br> | ||
<math>=\frac{e^ | <math>=\frac{e^t}{2}(cos(0) - sin(0)) -\frac{e^0}{2}(cos(t) - sin(t))</math><br> | ||
<math>=\frac{e^t}{2}-\frac{1}{2}(cos(t) - sin(t))</math><br> | |||
[[7.1 Integration By Parts/1|1]] | [[7.1 Integration By Parts/1|1]] | ||
Revision as of 02:33, 27 November 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f'(x)= \int_{0}^{t} e^s sin(t-s) \cdot ds }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - \int_{0}^{t} e^s cos(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle u= e^s ~ ~ ~ ~ ~ dv=sin(t-s)dx ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ u=e^s ~ ~ ~ ~ ~ dv=cos(t-s)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle du= e^s ds~ ~ v=cos(t-s) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ du=e^s ~ ~ ~ ~ ~ v=-sin(t-s)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s) -\int_{0}^{t} e^s \sin(t-s) \cdot ds}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 2\int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ e^s \cdot cos(t-s) - e^s \cdot sin(t-s)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{t} e^s sin(t-s) \cdot ds ~ ~ ~ = ~ ~ ~ \frac{e^s}{2}(cos(t-s) - sin(t-s)) \Bigg|_0^t}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =\frac{e^t}{2}(cos(0) - sin(0)) -\frac{e^0}{2}(cos(t) - sin(t))}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =\frac{e^t}{2}-\frac{1}{2}(cos(t) - sin(t))}
1 2 3 4 5 7 8 9 10 11 12 13 14 15 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 43 45 47 48 49 50 51 52 53 54 61 65