The answer is (1/2)xe^(2x) - (1/4)e^(2x) + C
Solution:
Since our given integrand is the product of the functions x and e^(2x), we can use the formula for integration by parts by choosing
u = x
dv/dx = e^(2x)
By differentiating u, we get
du/dx= 1
By integrating dv/dx= e^(2x), we have
v =∫e^(2x) dx = (1/2)e^(2x)
Then we substitute these values to the integration by parts formula:
∫ u(dv/dx) dx = uv −∫ v(du/dx) dx
∫ x e^(2x) dx = (x) (1/2)e^(2x) - ∫ ((1/2) e^(2x)) (1) dx
= (1/2)xe^(2x) - (1/2)∫[e^(2x)] dx
= (1/2)xe^(2x) - (1/2) (1/2)e^(2x) + C
where c is the constant of integration.
Therefore,
∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C
Answer:
D. ASA
Step-by-step explanation:
ASA (Angle-Side-Angle) is a proof of congruence when two triangles share two angles and the side between them.
The unit normal for the given plane is <5,2,-1>.
The equation of the plane parallel to the given plane passing through (5,5,4) is therefore
5(x-5)+2(y-5)-1(z-4)=0
simplify =>
5x+2y-z=25+10-4=31
Answer: the plane through (5,5,4) parallel to 5x+2y-z=-6 is 5x+2y-z=31
Answer:
A: 357
(1) 9641
Step-by-step explanation:
With A you really just want to go from the smallest number up so it would be the smallest number possible.
<em>EX.</em> 357 vs. 736 357 is smaller
With 1 you have to go from the highest number to lowest number to get the biggest answer possible.
<em>Ex.</em> 9641 vs. 1946 9641 is larger.
ounces of water
ounces of cocoa
ounces of water
ounces of cocoa (same amount of cocoa as before because pure water is being added)
ounces of water
ounces of cocoa