Question 4 [Integration by Substitution]: In each of thefollowing cases, the function to be integrated, β(π₯), can bewritten in the following form β(π₯) = π(π(π₯))πβ²(π₯) In each case,state the function π(π₯) (i.e. write an explicit form in terms ofπ₯), then, make the substitution π’ = π(π₯) and evaluate the definiteintegral β« β(π₯) ππ₯ (from a to a) by evaluating theequivalent integral over π’.
a) β(π₯) = cos(π₯) sin^3 (π₯) , π = 0, π = π/2
b) β(π₯) = 3π₯^2 sin(π₯^3 ) , π = 0, π = π
c) β(π₯) = 1/π₯ (ln^2 (π₯) β 1) , π = 1, π = 2, π₯ > 0.
(For parts b) and c) give your final answer as a decimal numberaccurate to 4 decimal places)
Question 4 [Integration by Substitution]: In each of the following cases, the function to be integrated, β(𝑥), can be wr
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answerhappygod
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