The area of the region bounded by the curve y= |x^3-4 x^2+3 x | and the x -axis, 0 ≤ x ≤ 3 , is -

Correct answer: (C) 37/12. A=∫_0^1 f(x) d x-∫_1^3 f(x) d x=∫_0^1 (x^3-4 x^2+3 x ) d x-∫_1^3 (x^3-4 x^2+3 x ) d x=37/12

Q41 / 90 · KVPY 2016 (SB/SX) · Mathematics

The area of the region bounded by the curve $y=\left|x^{3}-4 x^{2}+3 x\right|$ and the $x$-axis, $0 \leq x \leq 3$, is $-$

A
$\frac{37}{6}$
B
$\frac{9}{4}$
Correct answer
C
$\frac{37}{12}$
D
0

Solution

$A=\int_{0}^{1} f(x) d x-\int_{1}^{3} f(x) d x=\int_{0}^{1}\left(x^{3}-4 x^{2}+3 x\right) d x-\int_{1}^{3}\left(x^{3}-4 x^{2}+3 x\right) d x=\frac{37}{12}$

Hence, the correct answer is option: 'C'.

The area of the region bounded by the curve $y=\left|x^{3}-4 x^{2}+3 x\right|$ and the $x$-axis, $0 \leq x \leq 3$, is $-$

Solution

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