The rate of change of the volume of liquid, V V\,V in cm3\text{cm}^3cm3, in a hydraulic cylinder is modeled by the derivative dVdt=10t4−23t5+34\displaystyle \frac{dV}{dt} = 10t^4 - \frac{2}{3t^5} + \frac{3}{4}dtdV=10t4−3t52+43 for t>0t > 0t>0, where t t\,t is the time in seconds. Find the general expression for V V\,V by evaluating:
∫(10t4−23t5+34)dt \int \left( 10t^4 - \frac{2}{3t^5} + \frac{3}{4} \right) dt ∫(10t4−3t52+43)dtgiving each term in its simplest form.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.