5
Integrate:
Integral of sec²x = tan x, Integral of sec x tan x = sec x
Evaluate from 0 to pi carefully using limits → Result = 2
So 2I = pi × 2 = 2pi
Final Answer: I = pi
--- COMMON MISTAKE ---
Students forget that area can NEVER be negative. If the curve goes below the x-axis, the integral gives a negative value. Always take the absolute value (modulus) when finding area. Also, never confuse the definite integral VALUE with AREA — they are equal only when f(x) is above the x-axis.