Q. 114.2( 5 Votes )

Evaluate the foll

Answer :

Let us assume …………………………equation 1


Let x= tan θ thus


Differentiating both sides, we get,



Thus substituting old limits, we get a new upper limit and lower limit


For 1 = tan θ



For 0 = tan θ


0 = θ


substitute the values in equation 1


we get …………………….equation 2


trigonometric identity we know



Thus substituting in equation 2 we have



………………………equation 3


By property, we know that


Thus


.....equation 4


Trigonometric formula:



Thus


We know by trigonometric property:



thus



Substituting in equation 4





We know


Thus


......equation 6


We know



Adding equation 3 and equation 6


2 +


Thus


2


2


2



We know b and a being the upper and lower limits respectively.



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