Answer Happy

Question 4 [Integration by Substitution]: In each of the following cases, the function to be integrated, h(x), can be written in the following form h(x) = f(g(x))g'(x) In each case, state the function g(x) (i.e. write an explicit form in terms of x), then, make the substitution u = g(x) and evaluate the definite integral c) h(x) = b fºnc by evaluating the equivalent integral over u. a) h(x) = cos(x) sin³(x), a = 0, b = π/2 b) h(x) = 3x² sin(x³), a = 0, b = π X h(x) dx (In²(x) — 1), a = 1, b = 2, x > 0. (For parts b) and c) give your final answer as a decimal number accurate to 4 decimal places).