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:
a) 8 x 10^3 or 8000
b) 8 x 10^-2 or .08
Explanation: Refer to a guide on rounding sig figs
Answer:
<h3>D</h3>
Step-by-step explanation:
(1/40) - (1/x) = (1/60)
x = 1/(1/40) - (1/60)) =
<span>A.) 120</span> minutes
Its similar to the other question.
36x^2-49
this closely matches the binomial formula of (a+b)*(a-b)=a^2-b^2
so we know:
a^2=36x^2
a=6x
b^2=49
b=7
so (a+b)*(a-b)=(6x+7)*(6x-7)=36x^2-49
