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.​

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

Answers ( )

    0
    2021-10-10T03:00:20+00:00

    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.

Leave an answer

Browse

14:4+1-6*5-7*14:3+5 = ? ( )