Question

Which of the following integrals cannot be evaluated using a simple substitution? (4 points) Select one:

Answer 1

Answer:

b and c,       b and c are same

Step-by-step explanation:

Only a and d can be evaluated using simple substitution.

For a, integral of the square root of (x-1)dx i.e

let y = x-1

   dy = dx

 It becomes integral square root of ydy, ∫√ydy

which is can easily be evaluated and y is substituted back.

For d, integral of x times the square root of the quantity x squared minus 1

   let y= x squared minus 1

  then dy = 2xdx

          dx = dy/2x

It becomes integral x times square root of y dy/2x

                 ∫x√ydy/2x=∫√ydy/2=1/2∫√ydy which can easily be evaluated and y is substituted back