The rate of power consumption, $P (t)$ in kilowatts, of an industrial cooling system is modeled by the function

\sqrt{18t+45} e^{\sqrt{2t+5}}

where $\ge 0$ is the time in hours since the start of the shift.

By using the substitution $\sqrt{2t+5}$ , show that the total energy consumed in the interval $\le t \le 10$ , given by $dt\int_{2}^{10} P(t) \, dt$ , can be expressed in the form

\int_{a}^{b} k u^2 e^u \, du

where $a$ , $b$ and $k$ are integers to be found.

Hence find, by algebraic integration, the exact value of the total energy consumed between $t = 2$ and $t = 10$ , giving your answer in the form $p e^5 + q e^3$ where $p$ and $q$ are integers.

The rate of power consumption, $P (t)$ in kilowatts, of an industrial cooling system is modeled by the function

\sqrt{18t+45} e^{\sqrt{2t+5}}

where $\ge 0$ is the time in hours since the start of the shift.

By using the substitution $\sqrt{2t+5}$ , show that the total energy consumed in the interval $\le t \le 10$ , given by $dt\int_{2}^{10} P(t) \, dt$ , can be expressed in the form

\int_{a}^{b} k u^2 e^u \, du

where $a$ , $b$ and $k$ are integers to be found.

Hence find, by algebraic integration, the exact value of the total energy consumed between $t = 2$ and $t = 10$ , giving your answer in the form $p e^5 + q e^3$ where $p$ and $q$ are integers.

1 Pure Mathematics

Question 128

Markscheme

1 Pure Mathematics

Question 128

Markscheme

1 Pure Mathematics

Question 128

1 Pure Mathematics Questions

1 Pure Mathematics

Question 128

1 Pure Mathematics Questions