AP EAMCET · Maths · Definite Integration
If \(\mathrm{I}=\int_1^3 \sqrt{3+\mathrm{x}+\mathrm{x}^2} \mathrm{dx}\), then \(\mathrm{I}\) lies in the interval
- A \((2 \sqrt{5}, 2 \sqrt{15})\)
- B \((\sqrt{3}, 2 \sqrt{5})\)
- C \((\sqrt{23}, \sqrt{33})\)
- D \((2 \sqrt{15}, \sqrt{23})\)
Answer & Solution
Correct Answer
(A) \((2 \sqrt{5}, 2 \sqrt{15})\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int_1^3 \sqrt{3+\mathrm{x}+\mathrm{x}^2} \mathrm{dx}=\int_1^3 \sqrt{\left(\mathrm{x}+\frac{1}{2}\right)^2+\left(\frac{\sqrt{11}}{2}\right)^2} \mathrm{dx}\)…
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