The area bounded by the curve y = sin–1(sinx) and x-axis for x ∈ [0, 50π] is
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Given : area bounded by the curve y = sin⁻¹(sinx) and x-axis
To Find : Area if x ∈ [0, 50π]
Solution:
y = sin⁻¹(sinx)
=> sin y = sin x
Graph will be triangular shape as shown in figure.
y = sin⁻¹(sinx)
Principle Range of Sin⁻¹ is [ -π/2 , π/2]
=> y ∈ [ -π/2 , π/2]
x ∈ [0, 50π]
Hence we have Base = 50 π
Height = π/2 (below or above of x axis )
Area = (1/2) * 50 π * π/2
= 25π²/2
= 123.37 sq units
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