TMUA Rosie's Papers Set A Paper 1 · Question 9

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Rosie's Papers Set A Paper 1 · Q9

Paper 1Calculus

$f(x)$ is given by $f(x)=ax^b-cx^d$ , where $b$ and $d$ are positive integers with $b<d$ , and $f(x)$ is also given to have these below properties:

\int_0^1 f(x)\,dx=\frac12,\qquad\left.\frac{dy}{dx}\right|_{x=1}=0,\qquad f(1)=1.

Hence find $a+b+c+d$ .

6

8

10

12

EIt cannot be determined uniquely without an initial boundary condition for

f(0)

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