Question

on definite integral [o,pi/4] evaluate d^tannx/cos^2(x) dx

Answer 1

e^tanx

Answer 2

u = tan x , du = sec^2 dx
sec^2 is the same as 1 / cos ^2 dx
so we have e^ u du , the integral is e^u , or e^(tanx) , now plug back in upper and lower limits.
so we have
e^(tan pi/4) - e^(tan 0) = e^1 - e^0 = e - 1

Answer 3

integral e^ u = e^u + c , but we have upper and lower limits