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

Question

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

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4 days 2021-10-10T02:58:57+00:00 1 Answer 0 views 0

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