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  • 4 years ago

show geometrically why the integral of sqrt(2-x^2) in the interval (0,1) is equal to (pi/4)+(1/2)

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  1. dumbcow
    • 4 years ago
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    the function represents the upper half of a circle of radius sqrt2 at x=1, y =1, from unit circle we know that the angle is pi/4: tan pi/4 = y/x = 1 The area from 0 to 1 is the combined area of a 1/8 sector of circle plus a triangle of length and height of 1. |dw:1328166468103:dw|

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