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integral sin{lim(t tends to 0)(2x/pie)cot(inverse)(x/t*t)} take limit from -pie/2 to pie/2

integral sin{lim(t tends to 0)(2x/pie)cot(inverse)(x/t*t)}


take limit from -pie/2 to pie/2

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:0
I = \int_{-\pi /2}^{\pi /2}sin(\lim_{t\rightarrow 0}\frac{2x}{\pi }.\cot ^{-1}\frac{x}{t^{2}})dx
I = \int_{-\pi /2}^{\pi /2}sin(\lim_{t\rightarrow 0}\frac{2x}{\pi }.0)dx
I = \int_{-\pi /2}^{\pi /2}sin(0)dx
I = \int_{-\pi /2}^{\pi /2}0dx = 0
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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