A chemical engineer models the rate of heat loss $H (T)$ , in kilowatts per degree Celsius, from a specific pressurized vessel using the formula

\frac{2T^2 - 3T - 7}{T - 4}, \quad T > 4

where $T$ is the temperature of the vessel in degrees Celsius.

Write $H (T)$ in the form

\frac{C}{T - 4}

where $A$ , $B$ , and $C$ are integers to be found.

Hence use algebraic integration to show that the total heat loss between temperature $T = 5$ and $T = 7$ , given by $dT\int_{5}^{7} H(T) \, dT$ , is equal to

\alpha + \beta \ln 3

where $α\alpha$ and $β\beta$ are integers to be found.

A chemical engineer models the rate of heat loss $H (T)$ , in kilowatts per degree Celsius, from a specific pressurized vessel using the formula

\frac{2T^2 - 3T - 7}{T - 4}, \quad T > 4

where $T$ is the temperature of the vessel in degrees Celsius.

Write $H (T)$ in the form

\frac{C}{T - 4}

where $A$ , $B$ , and $C$ are integers to be found.

Hence use algebraic integration to show that the total heat loss between temperature $T = 5$ and $T = 7$ , given by $dT\int_{5}^{7} H(T) \, dT$ , is equal to

\alpha + \beta \ln 3

where $α\alpha$ and $β\beta$ are integers to be found.

1 Unit 1: Pure Mathematics A

Question 256

Markscheme

1 Unit 1: Pure Mathematics A

Question 256

Markscheme

1 Unit 1: Pure Mathematics A

Question 256

1 Unit 1: Pure Mathematics A Questions

1 Unit 1: Pure Mathematics A

Question 256

1 Unit 1: Pure Mathematics A Questions