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Area of region bounded by y=x|x| bounded by x-axis and x=1,x=-1

Area of region bounded by y=x|x| bounded by x-axis and x=1,x=-1

Grade:11

2 Answers

Aakash
110 Points
5 years ago
According to defination of mod x 
mod x is x for x greater then zero
and mod x is -x for x less then zero.
hence, y can convert to:
Therefore area between y, x=1,x=-1 is
       (2 due to symmetry w.r.t to y-axis)
Aakash
110 Points
5 years ago
According to defination of mod x 
mod x is x for x greater then zero
and mod x is -x for x less then zero.
hence, y can convert to:
y= \begin{Bmatrix} x^{2} & x\geq 0\\ -x^{2} & x< 0 \end{Bmatrix} 
 
Therefore area between y ,x=1,x=-1 is:
A=2\int_{0}^{1}x^{2}dx  multiply by 2 due to symmetry
A=2\begin{bmatrix} \frac{1}{3} \end{bmatrix}
 
due to symmetry area is:
 

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