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Question

# Assertion :Statement 1 If n is positive integer then ∫nπ0∣∣∣sinxx∣∣∣dx≥2π(1+12+13+....+1n) Reason: Statement 2 sinxx≥2π on (0,π/2)

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

## The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion∫nπ0∣∣∣sinxx∣∣∣dx=∫π0sinxxdx+∫2ππ|sinx|xdx+....+∫nπ(n−1)π|sinx|xdx∫π0sinxxdx+∫π0sinuπ+udu+∫π0sinuπ+2udu+∫π0sinuu+(n−1)πdu(Putting x−π=u in 2nd integral, x−2π=u in 3rd integtral...,)∫π0sinuu+(r−1)π≥∫π0sinuπ+(r−1)π=2rπr=1,2,...,n∴∫nπ0∣∣∣sinxx∣∣∣dx≥2π[1+12+...+1n]Statement 2 is true but is not a correct reason for the statement- 1

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