Question

The area bounded by the curve y = x |x|, x-axis and the ordinates x = - 1 and x = 1 is given by

0

$1 third$
$2 over 3$
$4 over 3$

Solution

2 over 3

We want to find the area bounded by the curve $straight y equals straight x space open vertical bar straight x close vertical bar comma$ x-axis and the ordinates x = -1 and x = 1
Required area = $integral subscript negative 1 end subscript superscript 1 space straight y space dx space equals space integral subscript negative 1 end subscript superscript 1 space straight x space open vertical bar straight x close vertical bar space dx$
$equals space integral subscript negative 1 end subscript superscript 0 open vertical bar straight x open vertical bar straight x close vertical bar close vertical bar space dx space plus space integral subscript 0 superscript 1 space straight x space open vertical bar straight x close vertical bar space dx$
$open square brackets because space space space open vertical bar straight x space open vertical bar straight x close vertical bar close vertical bar space equals space open vertical bar straight x close vertical bar space open vertical bar straight x close vertical bar space equals straight x squared close square brackets$
$equals space integral subscript negative 1 end subscript superscript 0 left parenthesis straight x squared right parenthesis dx plus integral subscript 0 superscript 1 straight x squared dx space equals space open square brackets straight x cubed over 3 close square brackets subscript negative 1 end subscript superscript 0 plus open square brackets straight x cubed over 3 close square brackets subscript 0 superscript 1 equals space open square brackets 0 minus fraction numerator left parenthesis negative 1 right parenthesis cubed over denominator 3 end fraction close square brackets plus open square brackets 1 third minus 0 close square brackets space equals space 1 third plus 1 third equals 2 over 3$

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Vector Algebra

The area bounded by the curve y = x |x|, x-axis and the ordinates x = - 1 and x = 1 is given by

0

$1 third$
$2 over 3$
$4 over 3$

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

The area bounded by the curve y = x |x|, x-axis and the ordinates x = - 1 and x = 1 is given by 0

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The area bounded by the curve y = x |x|, x-axis and the ordinates x = - 1 and x = 1 is given by

0

$1 third$
$2 over 3$
$4 over 3$