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:
b=136, c=44, d=44
Step-by-step explanation:
B is the same measure as A. C = D and A+B+C+D=360; C+D=88; C=44; D=44
Answer:
Step-by-step explanation:
<h3>i) simplify the complex fraction</h3>
<h3>ii) simplify the equation using cross multiplication</h3>
<h3>iii) swap the sides of the equation</h3>
<h3>iv) divide both sides of the equation by -6</h3>
<h3>v) simplify the fraction</h3>
Great White
White-angled sulphur
Large orange sulphur
Apricot sulphur
Answer:
C. 795.45 in^2
Step-by-step explanation:
The formula for the surface area of a cylinder is ...
SA = 2πr^2 +2πrh = 2πr(r +h)
For r=6 and h=15.1, the surface area is ...
SA = 2π(6)(6 +15.1) = π(12)(21.1) = 253.2π
SA ≈ 795.45 . . . . square inches
