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
<h2>
Answer: 1/5 or 0.2
_____________________________________</h2><h3>
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form: x = 1/5
Decimal Form:
x = 0.2</h3><h3>
______________________________________________</h3>
Hope this helps!
Also can I please have Brainliest...?
<em>Only if I'm right of course...</em>
Answer:
Step-by-step explanation:
all you have to do is divide each number by 4, 41, 42, 43, 44, 45, 46, 47, 48, 49 ,and 50 until you get a remainder of 1. what I mean is do 2 divided by all the number from 40 50 and do the same with 4,5,8 and 10 until you find one of them that has a remainder of 1. (is a lot of work sorry could't tell you the anwer)
Answer:
0.56 milligrams
Step-by-step explanation:
Put 6 where t is and do the arithmetic.
M(6) = 50·e^(-0.75·6) = 50·e^-4.5 ≈ 0.56 . . . . milligrams
The absolute value inequality for the graph is given as |x| < 4
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
The absolute value is given by:
|x - average| = distance to midpoint
From the graph:
x > -4 and x < 4
The midpoint is 0, hence Distance between -4 or 4 to midpoint (0) is 4
Average = (-4 + 4)/2 = 0
Hence:
|x - 0| = 4
|x| < 4
The absolute value inequality for the graph is given as |x| < 4
Find out more on equation at: brainly.com/question/2972832
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