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In this question, we need to evaluate the integral given by the integral of x square over 100 minus x square to the power 3 by 2.
00:10
.d .x.
00:12
So first of all, we will substitute x equals to 10 sine theta.
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So we will get by differentiating dx equals to 10 cosine theta.
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Now we will draw our right angle, triangle by the.
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This sine theta will be equal to x over 10.
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So we will take perpendicular as x and hypotenous as 10.
00:47
We drawn that triangle.
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Here the perpendicular is x and the hypoteness is 10.
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This is from sine theta will be x over 10 where sine theta is perpendicular over hypotenous.
00:58
So perpendicular is x and hypoteness is 10.
01:00
We will calculate the base by using pythagoras theorem.
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So the base will be 100 minus x square.
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Under the square root.
01:13
So now from this triangle, we can see that here the 100 minus x square to the power 3y 2 and x square will be replaced by the expressions of trigonometry having theta...