IMPROPER INTEGRALS WORKSHEET

Problem 1 :

Solution :

Dividing each term by cos²x

Let t = tan x

dt = sec² x dx

When x = 0 and x = π/2

t = tan 0 ==> t = 0

t = tan π/2==> t = ∞

Problem 2 :

Solution :

Let t = cot x

dt = -cosec² x dx

cosec² x dx = -dt

When x = 0 and x = π/2

t = cot 0 ==> t = ∞

t = cot π/2 ==> t = 0

Problem 3 :

Solution :

Let t = tan x

dt = sec²x dx

When x = 0 and x = π/2

t = tan 0 ==> t = 0

t = tan π/2 ==> t = ∞