Question

Find the first quadrant area bounded by the curves: y = arctanx, y = and 4 π x = 0. Q

Answer 1

Given: The correct boundaries are 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.