Determine ∫(10t4−6t3) dt\int \left( 10t^4 - \frac{6}{\sqrt[3]{t}} \right) \, dt ∫(10t4−3t6)dt.
The rate of change of the mass, MMM grams, of a synthetic crystal with respect to time, ttt hours, is modeled by the differential equation
dMdt=10t4−6t3,t>0 \frac{dM}{dt} = 10t^4 - \frac{6}{\sqrt[3]{t}}, \quad t > 0 dtdM=10t4−3t6,t>0After 8 hours of growth, the mass of the crystal is measured to be 65520 grams.
Find an expression for MMM in terms of ttt.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.