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Question : 77 of 160
Marks:
+1,
-0
Solution:
Consider the given integral.
I=‌dx Take
x=tan‌θ, then
dx=sec2θdθ Substitute in the above integral and change the limits accordingly.
I‌‌=‌‌sec2θdθ ‌‌=‌loge(1+tan‌θ)dθ Now, using the property
f(x)dx=f(a−x)dx I‌‌=‌loge(1+tan(‌−θ))dθ =‌‌‌loge(1+‌)dθ =‌‌‌loge(‌)dθ =‌‌‌loge(2)dx−‌loge(1+tan‌θ)dθ Further simplifying, we get
I=‌loge(2)−I 2I=‌loge(2) I=‌loge(2)
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