c4e7117.webp" data-orsrc="https://uploads-pracbee-ramanuj.s3.ap-south-1.amazonaws.com/pyq-question-images/batch-001/60f12c4e7117.webp" loading="lazy" style="max-width:100%;height:auto;display:block;margin:0 auto;max-height:40vh;vertical-align:baseline" alt="JEE Main 2024 (Online) 6th April Morning Shift Mathematics - Definite Integration Question 55 English Explanation">

$$\begin{aligned} & \left.=\left(1-x^7\right)^{k+1} \cdot x\right]_0^1-\int_0^1(k+1)\left(1-x^7\right)^k\left(-7 x^6\right) \cdot x d x \\ & =-7(k+1) \int_0^1\left(1-x^7\right)^k\left(-1+1-x^7\right) \\ & I_b=-7(k+1)\left[-l_a+l_b\right] \\ & \Rightarrow r_k=\frac{l_a}{I_b}=\frac{7 k+8}{7 k+7}=1+\frac{1}{7(k+1)} \\ & \frac{1}{7\left(r_k-1\right)}=(k+1) \\ & \Rightarrow \sum_{r=-1}^{10} \frac{1}{7\left(r_K-1\right)}=\sum_{r=1}^{10}(k+1)=\frac{11.12}{2}-1=65 \end{aligned}$$

19:T43b,

$$r_k=\frac{I_a}{I_b} \text {, जहाँ } I_a=\int_0^1\left(1-x^7\right)^k d x$$

JEE Main 2024 (Online) 6th April Morning Shift Mathematics - Definite Integration Question 55 Hindi Explanation

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