examday

Community mocks

Yotta Paper 1 · Q15

Paper 1CalculusFunctions & graphs

The function f(x)f(x) has the property that f(x)=f(6−x)f(x)=f(6-x) for all real xx. Given that:

(∫23f(x) dx)2+(∫46f(x) dx)2+(∫24f(x) dx)(∫02f(x) dx)−∫633f(x) dx=−2.\begin{aligned} &\left(\int_2^3 f(x)\,\dd x\right)^2+\left(\int_4^6 f(x)\,\dd x\right)^2\\ &\quad+\left(\int_2^4 f(x)\,\dd x\right)\left(\int_0^2 f(x)\,\dd x\right)-\int_6^3 3f(x)\,\dd x=-2. \end{aligned}

Find the sum of the possible values of ∫03f(x) dx\int_0^3 f(x)\,\dd x.

A−10-10
B−5-5
C−3-3
D00
E33
F55
G1010
H272\frac{27}2

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →