Moderate -0.5 This is a straightforward integration by substitution question requiring the standard technique of letting u = 3x + 1, adjusting limits, and integrating u^(1/2). It's slightly easier than average because it's a single-step substitution with simple arithmetic and no algebraic complications, though it does require proper handling of definite integral limits.
Must attempt \([ \ ]\) at \(x=0\) (not assume it is 0) and be using an integrated function
\(\to 16/9 - 2/9 = 14/9\) or \(1.56\)
Answer
Marks
A1 [4]
Fraction or decimal. (\(1.56+\)C loses this A1)
$\int_0^1 \sqrt{3x + 1}dx = (3x+1)^{5/3} + 1.5$ then $÷ 3$
| B1 M1 M1 | MI for $(3x+1)^{5/3} + 1.5$; For division by 3 |
$\to [ \ ]$ at $1 - [ \ ]$ at $0$
| M1 | Must attempt $[ \ ]$ at $x=0$ (not assume it is 0) and be using an integrated function |
$\to 16/9 - 2/9 = 14/9$ or $1.56$
| A1 [4] | Fraction or decimal. ($1.56+$C loses this A1) |
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