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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → 1 + ∫ 1 x t - 1 dt sin ⁡ ( x - 1 ) is equal to

Correct answer

0

Step-by-step solution

Given: lim x → 1 + ∫ 1 x ( t − 1 ) d t sin ( x − 1 ) Using L’Hospital’s rule and leibuitzrule, l = lim x → 1 + d d x ∫ 1 x ( t − 1 ) d t d d x sin x − 1 lim x → 1 + x − 1 cos x − 1 = 0 1 = 0

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