First break the L into two rectangular prisms and then find the volume for each prism. Then add those two volumes together to get the L.
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
first：76 ÷ 19/25=100
a:80 / 20 * 1 / 25 =0.16
b:80 * 5/4 =100
c:80 / 5 ÷ 1 / 4 =64
d:80 * 5/4 =100
e:80 * 4/5 =64
So I think both B and D should be the right answer
No, because the equation shows her answer. 30 and 2 combined equals 32, which is the answer. 32x4=128 and 128/4=32
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