All categories

3 years ago

Integral of (x^2)/(e^x^3)

Mathematics

1 answer:

Lesechka [4]3 years ago

5 0

$I=\displaystyle\int\frac{x^2}{e^{x^3}}\,\mathrm dx$

Substitute $y=x^3$ and $\mathrm dy=3x^2\,\mathrm dx$ . Then

$I=\displaystyle\frac13\int\frac{\mathrm dy}{e^y}=-\frac1{3e^y}+C=-\frac1{3e^{x^3}}+C$

You might be interested in

School Season Ticket Package Football State University $150 for 7 games University of Football $200 for 8 games Gridiron Univers

Alecsey [184]

Football State University = $21.42 for one game

University of Football = $25 for one game

Gridiron University = $29.16 for one game

Sports University = $31.25 for one game

Out of these, Football State University gives the best deal on football tickets.

5 0

4 years ago

Read 2 more answers

A market research group is interested in comparing the mean weight loss for two different popular diets. The researcher chooses

Degger [83]

Answer:

Step-by-step explanation:Jawo

5 0

3 years ago

From a large number of actuarial exam scores, a random sample of scores is selected, and it is found that of these are passing s

Mnenie [13.5K]

Supposing 60 out of 100 scores are passing scores, the 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

The lower limit is 0.5.
The upper limit is 0.7.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

60 out of 100 scores are passing scores, hence $n = 100, \pi = \frac{60}{100} = 0.6$

95% confidence level

So $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 - 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.5$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6 + 1.96\sqrt{\frac{0.6(0.4)}{100}} = 0.7$

The 95% confidence interval for the proportion of all scores that are passing is (0.5, 0.7).

The lower limit is 0.5.
The upper limit is 0.7.

A similar problem is given at brainly.com/question/16807970

5 0

3 years ago

Mr. Harrow has eight boys and six girls in his Honors Pre-calculus class. If he randomly chooses two students, one at a time, wh

Sergeu [11.5K]

Answer: 15/91 which is choice B

=================================================================

There are two methods to find this answer.

Method 1) We have 6 girls and 8+6 = 14 students. The probability of picking a girl is 6/14 = 3/7. After the first girl is chosen, we have 5 girls left out of 14-1 = 13 students overall. The probability of picking another girl (assuming the first selection was a girl) is 5/13. Multiply these probabilities: (3/7)*(5/13) = (3*5)/(7*13) = 15/91

--------------------

Method 2) We can use the nCr combination formula. Order does not matter.

We have nCr = 6 C 2 = 15 ways to pick 2 girls. See the attached image below for the steps (figure 1)

Out of nCr = 14 C 2 = 91 ways to pick 2 students. See the attached image below for the steps (figure 2)

So that's another way to get the answer 15/91.