Use the substitution `u = x + 1` to find `int xsqrt(x + 1)\ dx`. (3 marks)
Calculus, EXT1 C2 2020 SPEC1 2
Evaluate `int_(-1)^0 (1 + x)/sqrt(1 - x)\ dx`, using the substitution `u=1-x`. (3 marks)
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Calculus, EXT1 C2 SM-Bank 1 MC
With a suitable substitution, `int_1^5(2x - 1)sqrt(2x + 1)\ dx` can be expressed as
- `1/2 int_1^5 (u^(3/2) + u^(1/2))\ du`
- `2 int_3^11 (u^(3/2) + u^(1/2))\ du`
- `2 int_1^5 (u^(3/2) - 2u^(1/2))\ du`
- `1/2 int_3^11 (u^(3/2) - 2u^(1/2))\ du`
Calculus, EXT1 C2 2018 HSC 11f
Evaluate `int_-3^0 x/sqrt(1 - x) dx`, using the substitution `u = 1 - x`. (3 marks)
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Calculus, EXT1 C2 2016 HSC 11b
Use the substitution `u = x - 4` to find `int xsqrt(x - 4)\ dx`. (3 marks)
Calculus, EXT1 C2 2004 HSC 1e
Use the substitution `u = x − 3` to evaluate
`int_3^4 xsqrt(x − 3)\ dx.` (3 marks)
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Calculus, EXT1 C2 2015 HSC 11e
Use the substitution `u = 2x - 1` to evaluate `int_1^2 x/((2x - 1)^2)\ dx`. (3 marks)
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Calculus, EXT1 C2 2013 HSC 5 MC
Which integral is obtained when the substitution `u = 1 + 2x` is applied to `int x sqrt(1 + 2x)\ dx`?
(A) `1/4 int (u - 1) sqrt u\ du`
(B) `1/2 int (u - 1) sqrt u\ du`
(C) `int (u - 1) sqrt u\ du`
(D) `2 int (u - 1) sqrt u\ du`
Calculus, EXT1 C2 2010 HSC 1e
Use the substitution `u = 1 - x` to evaluate `int_0^1 x sqrt(1 - x)\ dx`. (3 marks)
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Calculus, EXT1 C2 2012 HSC 11d
Use the substitution `u = 2 - x` to evaluate `int_1^2 x (2 - x)^5\ dx`. (3 marks)
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