Answer:
Hello your question is incomplete attached is the missing part the second curve ; y = 3x is incomplete so i would solve the problem taking the second curve as ; y = 3x + 8 ( giving you the general methodology )
answer : y = ( 5,32) , x = ( -1,8 )
area of shaded region = 90.673
Step-by-step explanation:
The given curves ; [tex]y = x^2 - 4x\\y = 3x +8[/tex]
solving the above curves simultaneously
[tex]x^2-4x = 3x + 8[/tex]
x^2 - 7x - 8 = 0
( x + 1 )(x - 8 ) = 0
hence X = ( -1 , 8 )
Therefore y = 3x + 8
when x = -1 , y = -3 + 8 = 5
when x = 8 , y = 24 + 8 = 32
hence y = ( 5, 32 )
attached below is the sketched region
Integrating the curves to determine the shaded area in respect to x = ( -1, 8)
∫ [( 3x +8 ) - ( x^2 - 4x ) ] dx
∫ ( -x^2 +7x + 8 ) dx
= { - x^3/3 + 3x^2 + 8x }
= { - 8^3/3 + 3(64) + 64} - { -1^3/3 + 3 - 8 }
= {-170.66 + 192 + 64 } - { -1/3 - 5 }
= -170.66 + 192 + 64 + 5.333 = 90.673 ( area of the shaded region )
