Integration by Substitution - Area of a Circle (2011)
42.5 هزار بار بازدید -
12 سال پیش
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The equation of a circle
The equation of a circle centred at (0,0) and with radius r is y=(r^2-x^2)^0.5.
By integrating y w.r.t. x from x=0 to x=r, we get the area of quarter of a circle with radius r.
At 3:20 the substitution x=rsinθ is used where θ is the angle between r and the vertical side of the triangle.
We could also use the substitution x=rcosθ where θ is the angle between r and the x-axis.
By integrating y w.r.t. x from x=0 to x=r, we get the area of quarter of a circle with radius r.
At 3:20 the substitution x=rsinθ is used where θ is the angle between r and the vertical side of the triangle.
We could also use the substitution x=rcosθ where θ is the angle between r and the x-axis.
12 سال پیش
در تاریخ 1391/03/18 منتشر شده
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