Question

Find first quadrant area bounded by the curves using integration :
y = arctanx, y=π/4 and x=0.​

Answer 1

Given: The boundaries y = arc tan x, y=π/4 and x=0.​

To find: Find first quadrant area bounded by the curves given.

Solution :

• Now we have given the curves y = arc tan x, y=π/4 and x=0.​

• So integrating y = tan^-1 x , where limits are:

                  upper limit is y₂ = π/4 and lower limit is y₁ = 0

• The area bounded is:

              ∫ tanx dx    (here upper limit is y₂ = π/4 and lower limit is y₁ = 0)

              ln | sec x |   (here upper limit is y₂ = π/4 and lower limit is y₁ = 0)

                  ln(sec π/4) - ln(sec 0)

                  ln(√2) - ln(1)

                  ln(√2)

                  0.346

Answer:

             So the area bounded is 0.346 sq. units.