I follow you all the time and copy your every move, but you can’t touch me or catch me. What am I?

The answer is    (d) 7/2======we have    we also  have an integral      notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum:     notice that for the piecewise function f, the function has the equationf(x) = x when x  ≤ 0. so for the integral  , f(x) = x so it changes into      for the piecewise function f, the function has the equationf(x) = x+1  when x  > 0. for the integral  , we have    therefore, back to our splitted integral:    

Find  the  area  of the  region bounded  by the  curves y equals  the  inverse sine  of  x divided  by 4,  y  =  0, andx  = 4  obtained  by  integrating  with  respect  to  y.  your work must include  the  definite integral  and theantiderivative.