Solve This Definite Integral 🔥 | Answer = log|m|/(m²−1) | What Happens at m = 1?

In this video, we solve the following definite integral step by step: I = ∫₀^(π/2) [tan x / (1 + m² tan²x)] dx Using an appropriate substitution, we obtain the final result: log|m|/(m²−1) But the solution does not end here. An important question arises: What happens at m = 1? 🤔 When m = 1, the final expression log|m|/(m²−1) takes the indeterminate form 0/0. So, we investigate the m = 1 case using two different methods. 🔹 Method 1 — Put m = 1 directly into the original integral The original integral becomes I = ∫₀^(π/2) [tan x / (1 + tan²x)] dx We evaluate this particular integral separately and obtain: 1/2 🔹 Method 2 — Take the limit of the final answer We evaluate lim(m→1) [log|m|/(m²−1)] and once again obtain: 1/2 The fact that both approaches give the same value provides the final validation for the m = 1 case. This video is therefore not only about solving a definite integral, but also about understanding special cases, indeterminate forms, limits, and the validity of a resulting expression. 📚 Topics Covered ✅ Definite Integration ✅ Integration with Parameter m ✅ Substitution Method ✅ Trigonometric Integration ✅ Logarithmic Result ✅ Special Case m = 1 ✅ Indeterminate Form 0/0 ✅ Limits ✅ Validity of an Integral ✅ Class 12 Calculus ✅ JEE Main Mathematics ✅ JEE Advanced Mathematics Watch the complete video to see what happens to this integral at m = 1 #definiteintegration #Integration #Calculus #Mathematics #IntegrationTricks