The instantaneous power output P(t)P(t)P(t) of a specific alternating current component, measured in Watts, is modeled by the function:
P(t)=(3sin2t+5cos2t)2 P(t) = (3\sin 2t + 5\cos 2t)^2 P(t)=(3sin2t+5cos2t)2where ttt is the time in seconds. The total energy E(t)E(t)E(t) transferred by the component is given by E(t)=∫P(t) dtE(t) = \int P(t) \, dtE(t)=∫P(t)dt.
Determine the general expression for E(t)E(t)E(t) 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.
