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+92P(t) = 20t^3 - \frac{6}{5t^4} + \frac{9}{2}P(t)=20t3−5t46+29
where 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)dt
giving each term in its simplest form.
Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) 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.