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Show that the area of the ellipse in the accompanying figureis $\pi a b .[\text {Hint} \text { : Use a formula from geometry. }]$

$A=\pi a b$

Calculus 1 / AB

Calculus 2 / BC

Chapter 6

APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

Section 1

Area Between Two Curves

Integrals

Integration

Applications of Integration

Area Between Curves

Volume

Arc Length and Surface Area

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Lectures

01:11

In mathematics, integratio…

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In grammar, determiners ar…

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Area of an Ellipse Prove t…

05:22

Show that an ellipse with …

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Show that the area of the …

00:56

The area of the ellipse in…

01:46

You know that the area of …

06:32

Area of an ellipse The upp…

06:48

10:08

Area Find the area enclose…

01:00

Area Let $a > 0$ and $b…

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Area of an ellipse The are…

it was probably when I show that the area of an ellipse is pie A. B. So let's keep in mind that our lips would be X squared over. Let's say um One plus y squared over. We'll say four. It has to be a different value. If it's the same value will end up getting a circle equals one. So this gives us an ellipse and we see that by changing this, change the shape of it, this is going to be a squared and this is going to be b squared. So our area is going to be pie baby. one way we could show this with integral is by solving for why. Um If you solve for y you'll end up getting this equation right here. Subtract this multiplied by four. Um and then take the square root. When we take that square root, we'll have half of the area that we can find it and then we just double that.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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