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)
These intercepts<span> are plotted in Figure 3.1 and the line </span>3x<span> + </span>2y<span> = </span>12<span> is drawn through them. Figure 3.2: Adding the graph of </span>y<span> = </span>x<span> + 1. The second equation </span>y<span> = </span>x+ 1 has slope-intercept<span> form </span>y<span> = mx + b. Hence, the slope is m = 1 and the </span>y-intercept<span> is (0, 1).</span>
A refraction cup that is the shape of the semicircle will create a sphere if you put two of them together.
Hope this helps:)
The most helpful form to find the coordinates of the minimum is the vertex form.
<h3>Which form is better to find the minimum?</h3>
Remember that for a quadratic equation with a positive leading coefficient, the minimum is at the vertex.
So the better form to determinate the coordinates of the minimum value will be the vertex form, where if the vertex is (h, k), we get:
y = a*(x - h)^2 + k
In this case, the first option is in that form:
y = (x + 1)^2 - 25
so:
h = -1
k = -25
This means that the coordinates of the minimum are (-1, -25)
If you want to learn more about quadratic equations, you can read:
brainly.com/question/1214333
Obtuse
I think ......
I really hope this helps
And I hope that this is right
