KCET · Maths · Area Under Curves
The area of the region bounded by the line \(y=x+1\) and the lines \(x=3\) and \(x=5\) is
- A \(\frac{7}{2}\) sq units
- B \(\frac{11}{2}\) sq units
- C 7 sq units
- D 10 sq units
Answer & Solution
Correct Answer
(D) 10 sq units
Step-by-step Solution
Detailed explanation
\(\therefore\) Required area, \(A=\int_3^5(x+1) d x\)
\(\begin{aligned} & =\left[\frac{x^2}{2}+x\right]_3^5=\left[\frac{25}{2}+5-\frac{9}{2}-3\right] \\ & =\left[\frac{25+10-9-6}{2}\right]=\frac{20}{2} \\ & =10 \text { sq units }\end{aligned}\)
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