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:
Lori spends <u>9 minutes</u> on sketching 
th of a sketch.
Step-by-step explanation:
Given equation:
where 
number of minutes Lori spends on sketching
and 
number of sketches Lori makes.
We need to calculate the time spent by Lori in sketching of a sketch.
So we know the value of 
as 
represents number of sketches and in this situation Lori has sketched only a fraction of a painting.
So we plugin in the equation and calculate 
which is time spent by Lori sketching th of a sketch.
∴ 
minutes (Answer)
∴ Lori spends 9 minutes on sketching th of a sketch.
Answer:
d
Step-by-step explanation:
2x+3x-9-1
x
<em><u>
</u></em>
Answer:
Answer is 36cm
Step-by-step explanation:
Given:-
The perimeter of a square is 24 cm
To Find:-
It's Area
Solution:-
One side of the square
=24/4cm
=6cm
We know that, formula of the area of a square,
Area=(one side)^2
so,the area of the square=6^2cm=36
Important formula:-
•Perimeter of square=4×one side
•Perimeter of rectangle =2(length+breadth)
•Area of rectangle=length×breadth
I hope it's helpful!
