Evaluate the integral of root (9-x^2)dx from 3 to -3.

And

If the area of a semi circle is 0.7709 find an approximate for Pi. The semi circle has equation y = root (1-x^2). I get 1.5418 which is clearly wrong as Pi is 3.14

Evaluate the integral of root (9-x^2)dx from 3 to -3.

And

If the area of a semi circle is 0.7709 find an approximate for Pi. The semi circle has equation y = root (1-x^2). I get 1.5418 which is clearly wrong as Pi is 3.14
Hint for the first one: what shape is the graph of the function? (Alternative (slower) method: use a trigonometric substitution if you've learnt them.)

Originally Posted by InteGrand
Hint for the first one: what shape is the graph of the function? (Alternative (slower) method: use a trigonometric substitution if you've learnt them.)
It's a semi circle with x intercepts -3 and 3 and y int 9

It's a semi circle with x intercepts -3 and 3 and y int 9
Almost correct! (The y-intercept is not 9, but 3.) Does that help you with evaluating the integral (remembering that it is the "area under the curve")?

It's a semi circle with x intercepts -3 and 3 and y int 9

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Oh yes I meant y=3.

So is the integral from 3 to -3? And is it -2/3(9-x)^3/2 but when you sub x=3 and -3 the answer is zero

This is my solution. Can someone tell me where I am making a mistake. Cause the answer is 14.137 correct to 3 dp.

https://imgur.com/gallery/qLQ1s

It's 6b.

Oh yes I meant y=3.

So is the integral from 3 to -3? And is it -2/3(9-x)^3/2 but when you sub x=3 and -3 the answer is zero
Thats because you have to use a different approach, either try to do it the very easy way and just try to work out the area of the semi-circle (since its a simple shape which has an easy area to work out since you know its radius as InterGrand was hinting) or you could use trigonometric substitution subbing in x=3sinthetr or x=3costhetr

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Oh yes I meant y=3.

So is the integral from 3 to -3? And is it -2/3(9-x)^3/2 but when you sub x=3 and -3 the answer is zero
That is not the right antiderivative. We can't just use a "power rule" like that because there is an x2 term present.

It is easier to obtain the answer if you use a well-known formula for the area of a circle.

This is my solution. Can someone tell me where I am making a mistake. Cause the answer is 14.137 correct to 3 dp.

https://imgur.com/gallery/qLQ1s

It's 6b.
.

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Okay thank you. I didn't think we could use the formula.

For the second question, unless im not thinking straight the radius would have to be approximately 1/root 2 for the given area (i.e. 0.7709) to be correct which isnt the case since the radius would have to be 1 according to the given equation so either you made a mistake in typing up the question or the given question is just completely wrong or im just being a complete idiot and missing something

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