Answer Happy

Question 4 [Integration by Substitution]: In each of thefollowing cases, the function to be integrated, ℎ(𝑥), can bewritten 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 of𝑥), then, make the substitution 𝑢 = 𝑔(𝑥) and evaluate the definiteintegral ∫ ℎ(𝑥) 𝑑𝑥 (from a to a) by evaluating theequivalent integral over 𝑢.
a) ℎ(𝑥) = cos(𝑥) sin^3 (𝑥) , 𝑎 = 0, 𝑏 = 𝜋/2
b) ℎ(𝑥) = 3𝑥^2 sin(𝑥^3 ) , 𝑎 = 0, 𝑏 = 𝜋
c) ℎ(𝑥) = 1/𝑥 (ln^2 (𝑥) − 1) , 𝑎 = 1, 𝑏 = 2, 𝑥 > 0.
(For parts b) and c) give your final answer as a decimal numberaccurate to 4 decimal places)