Question

Find the area of the region enclosed by​ f(x) and the​ x-axis for the given function over the specified interval.

Answer 1

Answer:

Step-by-step explanation:

Complete Question

The complete question is  shown on the first uploaded image

Answer:

The  area is  $A =8 sq\cdot unit$

Step-by-step explanation:

     

   From the question we are told that

     The  first equation is $f(x) = x^2 + x \ \ \ x< 1$      

                                                                                    $on[ -2 , 3 ]$

      The  second equation is  $f(x) = 2 x \ \ \ x \ge 1$  

This means that the limit of the area under the enclosed region is limited between -2 to  1  on the x- axis  for first equation and  1 to  3 for second equation

    Now  the area under the region is evaluated as

                   $A = \int\limits^1_{-2}{x^2 + x } \, dx + \int\limits^3_{1}{2x } \, dx$

                   $A ={ \frac{x^3}{3} + \frac{x^2}{2} + c } | \left \ 1 } \atop {-2}} \right. + {\frac{2x^2}{2} }| \left \ 3} \atop {1}} \right.$

                  $A =9 + c - 1 -c$

                 $A =8 sq\cdot unit$