JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let \(\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}\). If \(\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathrm{N}\), then \(3(\mathrm{~b}+\mathrm{c})\) is equal to
- A \(22\)
- B \(39\)
- C \(40\)
- D \(26\)
Answer & Solution
Correct Answer
(B) \(39\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & I(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}} \\ & \text { Put } \frac{x-11}{x+15}=t \Rightarrow \frac{26}{(x+5)^2} d x=d t \\ & I(x)=\frac{1}{26} \int \frac{d t}{t^{1 / 13}}=\frac{1}{26} \cdot \frac{t^{2 / 13}}{2 / 13}\end{aligned}\)…
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