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
A model being 0.001 shaded would be 0.1% or 1/1000 of the whole model. 1 would equal the whole model being shaded, but that’s not the case. Instead, it’s in the thousandths, so that’s 1/1000 or 0.1% of the whole model shaded.
Answer:
∆WUV⁓∆SRT
Step-by-step explanation:
We know that PQ is 21 cm and QR is 5 cm. There are only 2 possible answer for this and you use only one formula. It's called the Pythagorean theorem.
The first possible is this. If the hypotenuse(the longest side of a triangle) is PR, we do:
a² + b² = c² ←Fill in the numbers
21² + 5² = c²
441 + 25 = c²
466 = c²
√466 = 21.12 cm←Possible length
The second possible is this:
5² + b² = 21²
25 + b² = 441
b² = 441 - 25
b² = 416
√416 = 20.4←Another possible answer
But what are they midpoints of? AFE, BFC, CEF,AFB?
