smc-1204-30-\(\large \text{sec}^2\)

Calculus, 2ADV C4 2020 HSC 13

Evaluate `int_0^(pi/4) sec^2 x\ dx`. (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

`1`

Show Worked Solution

`int_0^(pi/4) sec^2 x`	`= [tan x]_0^(pi/4)`
	`= tan\ pi/4-tan 0`
	`= 1`

Calculus, 2ADV C4 2008 HSC 2cii

Evaluate `int_0^(pi/12) sec^2 3x\ dx`. (3 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`1/3`

Show Worked Solution

`int_0^(pi/12) sec^2 3x\ dx`

`= [1/3 tan 3x]_0^(pi/12)`

`= [(1/3 tan (pi/4))-(1/3 tan 0)]`

`= 1/3(1)-0=1/3`

Calculus, 2ADV C4 2012 HSC 11g

Find `int_0^(pi/2) sec^2 (x/2)\ dx` (3 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`2`

Show Worked Solution

`int_0^(pi/2) sec^2 (x/2)\ dx`

`= [2 tan(x/2)]_0^(pi/2)`

`= 2 tan\ pi/4-2 tan 0`

`= 2(1)-0=2`