If f is continuous and / f(x) da = 50, find I = [f(4x) dx. Answer: I =Evaluate the given integral in terms of a, assuming a > 0:Evaluate the definite integral da ( 4 + 52 ) 2Each of the indefinite integrals below can be simplified by making a substitution. Choose an effective substitution in each case. To simplify the marking, consider only possible substitutions with one of the forms listed below, where m and b are integers: u(0) = mo + b, u(0) = emoto, u(0) = sin(me + b), u(0) = cos(me + b). (You may, of course, replace 0 with any other variable name.) Note: You are not expected to evaluate the final integral. (a) Which of the following substitutions will simplify / 1.6 cos(t) sin(t) at? Only u = cos(t). Only u = sin(t) Either u = cos(t) or u = sin(t). Neither u = cos(t) nor u = sin(t). 73 (b) For 5x + 4 dx , the substitution u = leads to the simpler integral / f(u) du, where f(u) = (c) For e" tan(e") dr, the substitution u = leads to the simpler integral / g(u) du where g(u) =In this problem you will evaluate the following definite integral using substitution: 1 16:2 , 27r da: 0 4127-rz+7r (a) First, choose an suitable substitution from the list below that would allow you to evaluate the integral: 2 u:4:p 771m+7r u16z27r u:412 16z27r u: 42221rz+1r (b) When you make the appropriate substitution from the list above, you will end up with an integral of the form 11 / f(u)du, where a