Asked by TayB
Evaluate the integral by making the given substitution. (Use C for the constant of integration.)
∫ dt/(1-7)^7, u=1-7t
∫ dt/(1-7)^7, u=1-7t
Answers
Answered by
Damon
I suspect you mean
∫ dt/(1-7t)^7, u=1-7t
so if u = 1-7t
then du = -7 dt
or dt = -du/7
so we have
∫( -du/7)/u^7
or
-(1/7) ∫ u^-7 du
-(1/7)(-1/6) u^-6
(1/42) u^-6 + C
1/[42(1-7t)^6] + C
∫ dt/(1-7t)^7, u=1-7t
so if u = 1-7t
then du = -7 dt
or dt = -du/7
so we have
∫( -du/7)/u^7
or
-(1/7) ∫ u^-7 du
-(1/7)(-1/6) u^-6
(1/42) u^-6 + C
1/[42(1-7t)^6] + C
There are no AI answers yet. The ability to request AI answers is coming soon!