KVPY SX SB Exam 2016 Question Paper

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Question : 14 of 120

Marks: +1, -0

The area of the region bounded by the curve

y = | x^3-4x^2 + 3x |

and the x-axis,

0 ≤ x ≤ 3

, is -

$37/6$
$9/4$
$37/12$
0

Solution:

A=∫↖{1}↙{0}f(x)dx-∫↖{3}↙{1}f(x)dx

=∫↖{1}↙{0} (x^3-4x^2+3x)dx

-∫↖{3}↙{1} (x^3-4x^2+3x)dx

=37/12

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