smc-1204-30-Sec^2

Calculus, 2ADV C4 2020 HSC 13

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

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`1`

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`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)

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`1/3`

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`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)

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`2`

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`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`