t-7-sin-t-7-dt-

Question Number 168291 by MikeH last updated on 07/Apr/22

$$\int{t}^{\mathrm{7}} \mathrm{sin}\left({t}^{\mathrm{7}} \right){dt} \\ $$

Answered by Engr_Jidda last updated on 07/Apr/22

let t^7 =x then dt=7t^6 dx ∴ ∫t^7 sin(t^7 )dt=∫7xsinx(x^(−1) )dx =7∫sinxdx=−7cosx OR −7cos(t^7 )

$${let}\:{t}^{\mathrm{7}} ={x}\:{then}\:{dt}=\mathrm{7}{t}^{\mathrm{6}} {dx} \\ $$$$\therefore\:\int{t}^{\mathrm{7}} {sin}\left({t}^{\mathrm{7}} \right){dt}=\int\mathrm{7}{xsinx}\left({x}^{−\mathrm{1}} \right){dx} \\ $$$$=\mathrm{7}\int{sinxdx}=−\mathrm{7}{cosx}\:{OR}\:−\mathrm{7}{cos}\left({t}^{\mathrm{7}} \right) \\ $$

Answered by Florian last updated on 07/Apr/22