KCET · Maths · Area Under Curves
The area bounded by the line \( y=x, x \)-axis and ordinates \( x=-1 \) and \( x=2 \) is
- A \( \frac{3}{2} \)
- B \( \frac{5}{2} \)
- C \( 12 \)
- D \( 13 \)
Answer & Solution
Correct Answer
(B) \( \frac{5}{2} \)
Step-by-step Solution
Detailed explanation
Given lines, \( y=x, y=0, x=-1 \) and \( x=2 \)
So, required area is given by
The area of shaded region
\[
\begin{array}{l}
=\frac{1}{2} \times|x|+\frac{1}{2} \times 2 \times 2 \\
=\frac{1}{2}+2=\frac{5}{2} \text { sq. units }
\end{array}
\]
So, required area is given by
The area of shaded region
\[
\begin{array}{l}
=\frac{1}{2} \times|x|+\frac{1}{2} \times 2 \times 2 \\
=\frac{1}{2}+2=\frac{5}{2} \text { sq. units }
\end{array}
\]
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