(B) Given the equation of the line $y=mx$ and the boundaries $x=1$ and $x=2$. The required area is given by the definite integral: $\text{Area} = \int

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(B) Given the equation of the line $y=mx$ and the boundaries $x=1$ and $x=2$. The required area is given by the definite integral: $\text{Area} = \int_{1}^{2} mx \, dx = 6$ $\Rightarrow m \left[ \frac{x^2}{2} \right]_{1}^{2} = 6$ $\Rightarrow \frac{m}{2} (2^2 - 1^2) = 6$ $\Rightarrow \frac{m}{2} (4 - 1) = 6$ $\Rightarrow \frac{3m}{2} = 6$ $\Rightarrow 3m = 12$ $\Rightarrow m = 4$

Class 12 Mathematics Application of Integration Area bounded by region of single curve

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The area of the region bounded by the lines $y=mx$,$x=1$,$x=2$,and the $x$-axis is $6$ sq. units. Then,the value of $m$ is:

KCET 2014 All KCET

A
$11$
B
$04$
C
$13$
D
$12$

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Application of Integration

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Area bounded by region of single curve

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The area of the region bounded by the lines $y=mx$,$x=1$,$x=2$,and the $x$-axis is $6$ sq. units. Then,the value of $m$ is:

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