Definite Integration Question 12
Question 12
- Let
be a differentiable function and . Then, the value of $\lim {x \rightarrow 1} \int{4}^{f(x)} \frac{2 t}{x-1} d t 8 f^{\prime}(1) 4 f^{\prime}(1) 2 f^{\prime}(1) f^{\prime}(1)$
(1990, 2M)
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Answer:
Correct Answer: 12. (a)
Solution:
- $\lim {x \rightarrow 1} \int{4}^{f(x)} \frac{2 t}{x-1} d t=\lim {x \rightarrow 1} \frac{\int{4}^{f(x)} 2 t d t}{x-1}$
[using L’ Hospital’s rule]