HELP ASAP!!! WILL MARK BRAINLIEST!
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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:
base = 2 m; height = 6 m
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
Given the information:
- base of 8 meters
- height of 6 meters
- top side length of 4 meters.
=> the height of one of the triangles equal to the the height of the trapezoid = 6 meters
=> the base of the triangles:
= (the base of the trapezoid - the top side length) / 2
= (8-4)/2
= 2
So the base and height of one of the triangles : base = 2 m; height = 6 m
Hope it will find you well.
the corresponding point on the graph of where
is
.
<u>Step-by-step explanation:</u>
We have , The point (-12,12) is on the graph of y=f(x). We need to Find the corresponding point on the graph of y=g(x) where g(x)= 1/3f(x) . Let's find out:
On function , a point
lies . Another function
.
According to question , as On function , a point
lies :
⇒
Now, Putting x = -12 in function we get:
⇒
⇒ {
}
⇒
⇒
Therefore, the corresponding point on the graph of where
is
.