If the integral from 0 to pi/2 of sec^2 (x/k) dx = k find k, where 0 < = k < = pi.

Question

Mathematics

Bobby Stevenson

16 August, 01:23

If the integral from 0 to pi/2 of sec^2 (x/k) dx = k find k, where 0 < = k < = pi.

+4

Answers (1)

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Nash Richard · Answer 1

k = 2

Step-by-step explanation:

Integral is [k*tan (x/k]

If its equal to k,

k*tan (x/k) = I

tan (x/k) = 1

x = pi/2 upper limit

x = 0 lower limit

tan (pi/2k) - tan (0) = 1

pi/2k = pi/4

So, k = 2