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:
95.5°F
Step-by-step explanation:
Given the regression equation :
y = 1.8x - 76.9 ; the relationship between temperature (°F) and number of ice cream sold
y = number of ice cream sold
x = temperature (°F)
The temperature when 95 iccream cones are sold will be ;
Here, y = 95
Using the model :
95 = 1.8x - 76.9
95 + 76.9 = 1.8x
171.9 = 1.8x
Divide both sides by 1.8
171.9 / 1.8 = x
95.5°F = x
Hence, temperature when 95 cones of ice-cream are sold is 95.5°F
Answer:
Step-by-step explanation:
As long as the two equations represent the same straight line on the coordinate plane (they overlap), there will be infinite many intersections and infinite number of solutions.
