Answer:
I= (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C (for a≠0)
Step-by-step explanation:
for
I= ∫x^n . e^ax dx
then using integration by parts we can define u and dv such that
I= ∫(x^n) . (e^ax dx) = ∫u . dv
where
u= x^n → du = n*x^(n-1) dx
dv= e^ax dx→ v = ∫e^ax dx = (e^ax) /a ( for a≠0 .when a=0 , v=∫1 dx= x)
then we know that
I= ∫u . dv = u*v - ∫v . du + C
( since d(u*v) = u*dv + v*du → u*dv = d(u*v) - v*du → ∫u*dv = ∫(d(u*v) - v*du) =
(u*v) - ∫v*du + C )
therefore
I= ∫u . dv = u*v - ∫v . du + C = (x^n)*(e^ax) /a - ∫ (e^ax) /a * n*x^(n-1) dx +C = = (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C
I= (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C (for a≠0)
Answer:
The answers are "(f+g)(x)> 3 for all values of x" and "(f+g)(x)<6 for all values of x".
Step-by-step explanation:
- If f(x) = 1x1 + 9 =10, then f(x) is a constant for every value of x, which means that y=f(x) will take the value of 10 no matter which value takes x.
- If g(x)= -6, then g(x) is a constant for every value of x, which means that it will take the value of -6 no matter the value of x.
- (f+g)(x)=10 + (-6) = 10 - 6= 4. Then, no matter the value of x, the function (f+g)(x) will equal 4 (a constant).
- According to the available options, both "(f+g)(x)>3" and "(f+g)(x)<6" are true, because (f+g)(x)=4>3 and (f+g)(x)=4 <6.
Answer:
3
Step-by-step explanation:
6L/1.89L =3.174 bottles so 3 bottle is almost 6L
Answer:
The answer is c. 8 hours
Step-by-step explanation:
Since her battery dropped 25% in 2 hours then for it to drop 100% would take 8 hours.
25%+25%+25%+25%= 100%
so with this logic
25%= 2 hours
2+2+2+2=8
Hoped this helped !
Cheers, Z
