Calculate the area of the plane region bounded by the graph of y=sinx , the X-axis and the vertical line x=5π/2
- رياضيات
- 2021-05-04
- HebaAallahFathy
Calculate the area of the plane region bounded by the graph of y=sinx , the
X-axis and the vertical line x=5π/2
الأجوبة
From the fig. it is clear that sinx=0 at x=0 ,π,2π and sinx≥0 in the intervals[0,π] and [2π,5π/2], but sinx≤0 in the interval[π,2π], thus the required area is:
A=∫_a^b〖f(x)〗 dx=∫_0^(5π/2)|sinx | dx=∫_0^πsinx dx-∫_π^2πsinx dx+∫_2π^(5π/2)sinx dx
=-|cosx |_0^π-[-cosx ]_π^2π+[-cosx ]_2π^(5π/2)
-(cosπ-cos0 )-(-cos2π+cosπ )+(-cos〖5π/2〗+cos2π )
=-(-1-1)-(-1-1)+(0+1)=5 square units.
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