7/8/13 Example 1 | Plane Areas in Rectangular Coordinates | Integral Calculus Review

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Example 1 | Plane Areas in Rectangular Coordinates

Tags: horizontal strip vertical strip plane areas limits of integration dow nw ard parabola parabolic segment

Example 1

Find the area bounded by the curve y = 9 - x2 and the x-axis.

Solution

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Step 1: Sketch the curve.

→ downward parabola; vertex at (0, 9); latus rectum = 1

The required area is symmetrical with respect to the y-axis, in this case, integrate the half of the area then double the result to get the total

area. The use of symmetry will greatly simplify our solution most especially to curves in polar coordinates.

Using Horizontal Strip

Step 2: Determine the limits of the strip.

The strip shown will start from y = 0 and end to y = 9

Step 3: Apply the appropriate formula then integrate.

Where

7/8/13 Example 1 | Plane Areas in Rectangular Coordinates | Integral Calculus Review

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Submitted by Romel Verterra on February 22, 2010 - 11:54pm

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answer

Using Vertical Strip

Click here to show or hide the solution

Step 2: Determine the limits of the strip.

In this case the limits are not defined; we need to solve the points of intersection of the curves.

when y = 0, x = ± 3. The strip will swipe from x = 0 to x = 3.

Step 3: Apply the appropriate formula then integrate.

Where

okay!

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