Which of the expressions are equivalent to the one below? Check all that
1 answer:
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_______________
Evaluate the indefinite integral:
Make a trigonometric substitution:
so the integral (i) becomes
Now, substitute back for t = arcsin(x²), and you finally get the result:
✔
________
You could also make
x² = cos t
and you would get this expression for the integral:
✔
which is fine, because those two functions have the same derivative, as the difference between them is a constant:
![\mathsf{\dfrac{1}{2}\,arcsin(x^2)-\left(-\dfrac{1}{2}\,arccos(x^2)\right)}\\\\\\ =\mathsf{\dfrac{1}{2}\,arcsin(x^2)+\dfrac{1}{2}\,arccos(x^2)}\\\\\\ =\mathsf{\dfrac{1}{2}\cdot \left[\,arcsin(x^2)+arccos(x^2)\right]}\\\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{\pi}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5C%2Carcsin%28x%5E2%29-%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D%5C%2Carccos%28x%5E2%29%5Cright%29%7D%5C%5C%5C%5C%5C%5C%0A%3D%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5C%2Carcsin%28x%5E2%29%2B%5Cdfrac%7B1%7D%7B2%7D%5C%2Carccos%28x%5E2%29%7D%5C%5C%5C%5C%5C%5C%0A%3D%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cleft%5B%5C%2Carcsin%28x%5E2%29%2Barccos%28x%5E2%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%3D%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D)
✔
and that constant does not interfer in the differentiation process, because the derivative of a constant is zero.
I hope this helps. =)
_______________
Evaluate the indefinite integral:
Make a trigonometric substitution:
so the integral (i) becomes
Now, substitute back for t = arcsin(x²), and you finally get the result:
________
You could also make
x² = cos t
and you would get this expression for the integral:
which is fine, because those two functions have the same derivative, as the difference between them is a constant:
and that constant does not interfer in the differentiation process, because the derivative of a constant is zero.
I hope this helps. =)
Answer:
The p-value of the test is of 0.0536 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the executive's claim.
Step-by-step explanation:
A publisher reports that 75% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage.
At the null hypothesis, we test if the proportion is of 75%, that is:
At the alternate hypothesis, we test if the proportion is different of 75%, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
75% is tested at the null hypothesis:
This means that
A random sample of 280 found that 70% of the readers owned a particular make of car.
This means that
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion differing from 0.75 by at least |0.7 - 0.75| = 0.05, which is P(|z| > 1.93), which is 2 multiplied by the p-value of z = -1.93.
Looking at the z-table, z = -1.93 has a p-value of 0.0268.
2*0.0268 = 0.0536.
The p-value of the test is of 0.0536 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the executive's claim.