smc-1203-10-Exponential (Indefinite)

Calculus, 2ADV C4 2020 HSC 4 MC

What is `int e + e^(3x)\ dx`?

`ex + 3e^(3x) + c`
`ex + 1/3e^(3x) + c`
`e + 3e^(3x) + c`
`e + 1/3e^(3x) + c`

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`B`

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`int e + e^(3x) = ex + 1/3e^(3x) + c`

`(text(Note)\ e\ text(is a simple constant here))`

`=> B`

Calculus, 2ADV C4 2019 MET1-N 3

Evaluate `int_0^1 e^x - e^-x\ dx`. (2 marks)

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`e + (1)/(e) – 2`

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`int_0^1 e^x – e^-x\ dx`	`= [e^x + e^-x]_0^1`
	`= [e + (1)/(e) – (1 + 1)]`
	`= e + (1)/(e) – 2`

Calculus, 2ADV C4 2006 HSC 2bi

Find `int 1 + e^(7x)\ dx`. (2 marks)

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`x + 1 /7 e^(7x) + c`

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`int 1 + e^(7x) \ dx = x + 1/7 e^(7x) + c`

Calculus, 2ADV C4 2014 HSC 4 MC

Which expression is equal to `int e^(2x)\ dx`?

`e^(2x) + C`
`2e^(2x) + C`
`(e^(2x))/2 +C`
`(e^(2x + 1))/(2x + 1) + C`

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`C`

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`int e^(2x)\ dx`

`= 1/2 e^(2x) + C`

`=> C`

Calculus, 2ADV C4 2013 HSC 11e

Find `inte^(4x+1)dx` (2 marks)

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`1/4e^(4x+1)+C`

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`inte^(4x+1)\ dx=1/4e^(4x+1)+C`