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)
According to empirical rule, the area under the normal distribution or "bell-shaped curve", when plotted as a function of the z-parameter can be defined in terms of percentages.
The z-parameter (or z-score) is defined as
where
x = value of random variable,
μ = the mean,
σ = standard deviation,
The total area under the curve = 1.
The curve below shows that within 2 standard deviations from the mean, the total area under the curve is 95% of the total area.
Answer:
95%
Y - 63 = 1/2 (x - 64) (distribute 1/2)
y - 63 = 1/2x - 32 (add 63 to both sides)
y = 1/2x + 31 (this is your answer)
3x + 4y = 18......(2,3)
3(2) + 4(3) = 18
6 + 12 = 18
18 = 18...correct
2x - 2y = 2....(2,3)
2(2) - 2(3) = 2
4 - 6 = 2
-2 = 2...incorrect
when (2,3) is subbed into equation 1, it is true
when (2,3) is subbed into the second equation, it is false
the ordered pair (2,3) is not a solution to the system of linear equations
Make a rectangle that is 10 squares by 10 squares and color in 11 squares.