A chemical reactor's internal pressure PPP, measured in kilopascals (kPa), increases over time ttt (minutes) according to the model
P=34t2+12,t≥0 P = \frac{3}{4}t^2 + 12, \quad t \ge 0 P=43t2+12,t≥0A monitoring system tracks the pressure until it reaches a critical threshold of 39 kPa. The finite region R R\,R in the first quadrant of the ttt-P P\,P plane is bounded by the PPP-axis, the horizontal line P=39P = 39P=39, and the curve representing the reactor's pressure.
Calculate the exact area of RRR.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
