The slope of this ordered pair is 1.
Pythagorean theorem: a²+b²=c²
Where c = length of the hypotenuse (diagonal of a triangle)
60²+40²=c²
3600+1600=c²
5200=c²
c=√5200
c ≈ 72.11 ft
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:
Ok so I made up a fraction 7/5
! The result can be shown in multiple forms.
Exact Form:
7/6
Decimal Form:
1.16
Mixed Number Form:
1 1/6
Answer:
(-4, 1)
Step-by-step explanation:
