KCET · Maths · Sets and Relations
The area of the region bounded by the lines \( y=m x, x=1, x=2 \), and \( x \) axis is \( 6 \) sq. units, then
' \( \mathrm{m} \) ' is
- A \( 11 \)
- B \( 04 \)
- C \( 13 \)
- D \( 12 \)
Answer & Solution
Correct Answer
(B) \( 04 \)
Step-by-step Solution
Detailed explanation
Given that, equation of line \( y=m x, x=1 \) and \( x=2 \)
So, required area is given by
\(\text {Area}=\int_{1}^{2} m x d x=6 \)
\( \Rightarrow\left[m \frac{x^{2}}{2}\right]_{1}^{2}=6 \)
\( \Rightarrow m\left(2^{2}-1^{2}\right)=12 \)
\( \Rightarrow 3 m=12 \Rightarrow m=4\)
So, required area is given by
\(\text {Area}=\int_{1}^{2} m x d x=6 \)
\( \Rightarrow\left[m \frac{x^{2}}{2}\right]_{1}^{2}=6 \)
\( \Rightarrow m\left(2^{2}-1^{2}\right)=12 \)
\( \Rightarrow 3 m=12 \Rightarrow m=4\)
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