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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:
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________
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. =)
Answer:
linear model
Step-by-step explanation:
linear graph will produce a straight line
Considering the given figure, the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other is: In parallelogram EFGH show EK is congruent to KG and F.K is congruent to KH
<h3>How to determine the correct rephrase of the proof about parallelogram diagonals</h3>
The diagonals refer to the lines running between the two opposite ends of the parallelogram
Bisecting means sharing into two equal parts
congruent means a copy that is equal in dimension hence can be used in place of the other image
The diagonals of a parallelogram bisect each other means that the diagonals cut each other to form two equal parts such that each part is congruent to each other.
Learn more on diagonals of a parallelogram
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The minimum value for 2x is 0
<span>the maximum value is achieved when A, D and C are collinear and the quadrilateral ABCD becomes an isosceles triangle ABC </span>
<span>base AB = 52 and vertical angle 2x + 34° </span>
<span>For the sine law </span>
<span>(sin 2x)/22 = (sin ADB)/AB </span>
<span>(sin 34°)/30 = (sin BDC)/BC </span>
<span>is given that AB = BC, and sin ADC = sin BDC because they are supplementary, so from </span>
<span>(sin ADC)/AB = (sin BDC)/BC </span>
<span>it follows </span>
<span>(sin 2x)/22 = (sin 34°)/30 </span>
<span>sin 2x = 22 (sin 34°)/30 </span>
<span>2x = asin(22 (sin 34°)/30) ≈ 24.2° </span>
<span>x = 0.5 asin(22 (sin 34°)/30) ≈ 12.1° </span>
<span>0 < x < 12.1°</span>
Answer:
21.6 or 22
Step-by-step explanation:
Triangles have same angles. This means that they are proportion.
50/27 = 40/x
when you cross multiply to solve x, 50x = 1080
so x = 21.6
If you have to nearest whole number, it will be 22
