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V125BC [204]
3 years ago
11

Evaluate ∫ xe2x dx.

Mathematics
2 answers:
mixer [17]3 years ago
6 0
The formula is integral of (udv) = uv - integral of (vdu)
We use integration by parts by letting u = x and dv = (e^2x)dx
Then du = dx, and v = (1/2)(e^2x)
integral of x(e^2x)dx = (1/2)(x)(e^2x) - integral of (1/2)(e^2x)dx
= (1/2)(x)(e^2x) - (1/4)(e^2x) + C
Therefore the correct answer is C.
Helen [10]3 years ago
6 0
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 = xdv/dx = e^(2x)

By differentiating, 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, our simplified answer is now
<span>     ∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C</span>
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Answer:

2

Step-by-step explanation:

6 0
3 years ago
Mr. Weiler has 32 students in his class he wishes to place them into 8 groups of equal size. Which of the following represents t
SCORPION-xisa [38]

option 4: 4

8x4=32

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8 0
3 years ago
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A space shuttle orbits Earth at a speed of 21,000 km/hr. How far will it travel in 5 hours?
tresset_1 [31]
<span>21,000*5
since it travels 21,000 per hour and there is five hours. it's just simple substitution.
105,000 is the correct answer.</span>
7 0
3 years ago
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5000 people went to vote. Candidate Smith claimed 52% of the votes. Candidate Adams claimed 2681 votes. What percentage does can
boyakko [2]

The percentage of votes claimed by Adam is 53.62 %

<em><u>Solution:</u></em>

Given that, 5000 people went to vote

Candidate Smith claimed 52% of the votes. Candidate Adams claimed 2681 votes

To find: Percentage claimed by Adam

From given,

Total number of votes = 5000

Votes claimed by Adam = 2681

<em><u>The formula used is:</u></em>

Percentage\ claimed\ by\ Adam = \frac{\text{votes claimed by adam}}{\text{Total number of votes}} \times 100

<em><u>Substituting the values we get,</u></em>

Percentage\ claimed\ by\ Adam = \frac{2681}{5000} \times 100\\\\Percentage\ claimed\ by\ Adam = 0.5362 \times 100\\\\Percentage\ claimed\ by\ Adam = 53.62

Thus percentage of votes claimed by Adam is 53.62 %

3 0
3 years ago
The breaking strengths of cables produced by a certain manufacturer have a mean, u, of 1750 pounds, and a standard deviation of
AlladinOne [14]

Answer:

We accept the null hypothesis that the  breaking strength mean is less and equal to 1750 pounds and has not increased.

Step-by-step explanation:

The null and alternative hypotheses are stated as

H0:  u ≥ 1750   i.e the mean is less and equal to 1750

against the claim

Ha: u > 1750  ( one tailed test)  the mean is greater than 1750

Sample mean = x`= 1754

Population mean = u = 1750

Population deviation= σ = 65 pounds

Sample size= n = 100

Applying the Z test

z= x`- u / σ/ √n

z= 1754- 1750 / 65/ √100

z= 4/6.5

z= 0.6154

The significance level alpha = 0.1

The z - value at 0.1 for one tailed test is ± 1.28

The critical value is z > z∝.

so

0.6154 is < 1.28

We accept the null hypothesis that the  breaking strength mean is less and equal to 1750 pounds and has not increased.

8 0
3 years ago
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