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Exercise 25(c), p.113, question 7 Solve the differential equation d^2x/dt^2 + 16x =0 subject to the conditions x=3 and dx/dt = 16 when t=0. Find the maximum displacement and the maximum speed if x metres is the displacement of a particle moving in a straight line at time t seconds. How is...

Hello. I cannot make sense of these two similar questions. from Cambridge 3 Unit Year 11, p.434, q10. A cone is generated by rotating the line y=2x about the x-axis between x=0 and x=3. Using the trapezoidal rule with four function values, estimate the volume of the cone. from Cambridge...

Am I right in thinking that the only way to evaluate the definite integral y=sqrt(9-x^2) from -3 to 3 is Simp/ Trap rule or by using formula for area of semicircle or by using substitution where x =3sin theta? Are there any other ways? (from the ext 1 course?)