Question

The area bounded by the curve \(y=x|x|\),\(x\)-axis and the ordinates \(x=–1\) and \(x=1\) is given by
[Hint:\(y=x^2\, if\, x>0\) and \(y=–x^2\) if \(x<0]\)

• A. 0
• B. \(\frac{1}{3}\)
• C. \(\frac{2}{3}\)
• D. \(\frac{4}{3}\)

Answer 1

The Correct Option is C

The correct answer is:\(\frac{2}{3}units\)

Required area\(=∫^1_{-1}ydx\)
\(=∫^1_{-1}x|x|dx\)
\(=∫^0_{-1}x^2dx+∫^1_0x^2dx\)
\(=[\frac{x^3}{3}]^0_{-1}+[\frac{x^3}{3}]^1_0\)
\(=-(-\frac{1}{3})+\frac{1}{3}\)
\(=\frac{2}{3}units\)
Thus,the correct answer is C.