A researcher is interested in testing the perceived effort (PE) of runners under three different terrains. PE is measured on a s
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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:
Step-by-step explanation:
The correct question is
Large cheese pizzas cost $5 each and large one-topping pizzas cost $6 each.
Write an equation that represents the total cost, T, of c large cheese pizzas and d large one-topping pizzas.
Let
T -----> the total cost
c ----> the number of large cheese pizzas
d ---> the number of large one -topping pizzas
we know that
The total cost (T) is equal to the number of large cheese pizzas (c) multiplied by it cost ($5) plus the number of large one -topping pizzas (d) multiplied by it cost ($6)
Answer:
Step-by-step explanation:
The confidence interval for the difference of two population proportion is given by :-
Given : The first sample consists of 20 people with 9 having a common attribute.
Here, ,
,
Significance level :
Critical value :
A 95% confidence interval for the difference of two population proportion will be :-