Johann Carl Friedrich Gauss 1777 – 1855 Gauss worked in a wide variety of fields in both mathematics and physics including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His work has had an immense influence in many areas.
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Johann Carl Friedrich Gauss 1777 – 1855 Johann Carl Friedrich Gauss 1777 – 1855 Gauss worked in a wide variety of fields in both mathematics and physics.
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Johann Carl Friedrich Gauss1777 – 1855
Gauss worked in a wide variety of fields in both mathematics and physics including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His work has had an immense influence in many areas.
Decide on vertical or horizontal strips connecting the boundary curves. (Pick whichever is easier to write formulas for the length of the strip, and/or whichever will let you integrate fewer times.)
2
3 Write an expression for the area of the strip.(If the width is dx, the length must be in terms of x. If the width is dy, the length must be in terms of y.
4 Find the limits of integration. (If using dx, the limits are x values; if using dy, the limits are y values.)
5 Integrate to find area.
Examples:21) Find the area of the region enclosed by the curves 5 0, ,
1, and 2.x y x y
y y
2) Find the area of the region enclosed by the curves sin and sin 2 over the interval 0, .
y xy x
3) Find the area of the region enclosed by the curves below.