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:
The length of the pendulum is 14.13 meters.
Step-by-step explanation:
The length of a pendulum is given by the formula, 
, where T is the times period and L is the length of the pendulum.
Now, given that T = 2.4π seconds.
So, from the above equation, we get,
⇒ 
⇒ 
{We have the value of g as 9.81 m/sec²}
⇒ L = 1.44 × 9.81 = 14.13 meters. (Approx.)
Therefore, the length of the pendulum is 14.13 meters. (Answer)
Answer:
irrational
Step-by-step explanation:
It cannot be expressed as a fraction
Line was the problem, they’re supposed to subtract 10 not add 10
Answer:
y ≠ 9, y ≠ 3
Step-by-step explanation:
y² -12y +27 = (y - 9) (y - 3)
Denominator ≠ 0
y ≠ 9 or y ≠ 3
