Area bounded by the curves is 2.545 unit².
How to determine area between two curves.
Given that
y = x, y = 4x/x² + 1
x = 4x/x² + 1
x³ + x = 4x
x³ - 3x = 0
x(x² - 3) = 0
x = 0
x² = 3
x = +-√3
The limits are between -√3 to √3.
Area = ∫ₐⁿ(f(x) - g(x))dx
where
a = -√3 and n =√3
A = ∫ₐⁿ(x - 4x/x² + 1)dx
= ∫ₐⁿ(xdx - 4x/x² + 1dx)
Let u = x² + 1
du = 2xdx
Substitute
= ∫ₐⁿ(x - 2[1/udu])
= [x²/2 - lnu]ₐⁿ
= [x²/2 - ln(x² + 1)]ₐⁿ
Substitute the limits
= [(√3)²/2 - ln(√3)² + 1) - (-√3)²/2 - ln(-√3)² + 1)]
= 2.545 unit²
Therefore, area bounded by the curves is 2.545 unit².
Complete question