The rate at which a submersible drone consumes battery power, P(t)P(t)P(t) in watts, is modeled by the function:
P(t)=20t3−65t4+92 P(t) = 20t^3 - \frac{6}{5t^4} + \frac{9}{2} P(t)=20t3−5t46+29where t>0t > 0t>0 is the duration of the mission in hours. Find an expression for the total energy consumption by evaluating the indefinite integral:
∫(20t3−65t4+92)dt \int \left( 20t^3 - \frac{6}{5t^4} + \frac{9}{2} \right) dt ∫(20t3−5t46+29)dtgiving each term in its simplest form.
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.
