The rate of a chemical reaction, $r$ grams per minute, is modelled by the function

t^{1.5}, \quad t \ge 0

where $t$ is the time in minutes since the reaction began. A plot of this rate shows a curve starting at the origin, reaching a peak production rate at the point $M$ , and then falling back to zero at the point $P$ .

Using calculus, find the coordinates of the maximum point $M$ .

The reaction concludes when the rate returns to zero at point $P$ . Use algebra to find the $t$ -coordinate of $P$ .

The finite region $R$ is bounded by the curve, the horizontal line passing through $M$ , and the vertical line passing through $P$ .

Use algebraic integration to find the area of $R$ , giving your answer to two decimal places.

The rate of a chemical reaction, $r$ grams per minute, is modelled by the function

t^{1.5}, \quad t \ge 0

Using calculus, find the coordinates of the maximum point $M$ .

The reaction concludes when the rate returns to zero at point $P$ . Use algebra to find the $t$ -coordinate of $P$ .

The finite region $R$ is bounded by the curve, the horizontal line passing through $M$ , and the vertical line passing through $P$ .

Use algebraic integration to find the area of $R$ , giving your answer to two decimal places.

1.8 Integration

Question 86

Markscheme

1.8 Integration

Question 86

Markscheme

1.8 Integration

Question 86

1.8 Integration Questions

1.8 Integration

Question 86

1.8 Integration Questions