Answer:
volume of the solid is 3.180
Step-by-step explanation:
given data
line x + y = 2
parabola x2 + y = 4
to find out
the volume of the solid
solution
we draw a graph between line and parabola as show in fig given below attach
line cut at (-1,3) and (2,0)
so the length of diameter is ( 4 - x²) - (2 - x)
and radius of this semi circle will be ( 4 - x² - 2 + x ) /2
radius = (-x² + x + 2 ) /2
and r(x) will be = (-x² + x + 2 ) /2
and A(x) will be = π ( r(x)² ) /2
we will integrate from -1 to 2
= [tex]\int_{-1}^{2}A(x))[/tex]
= [tex]\int_{-1}^{2}(π ( (-x² + x + 2 ) /2)² ) /2))[/tex]
= 81π / 20
volume of the solid is 3.180
the decimal answer in the above answer is correct, but the fraction is wrong. it's [tex]\frac{81\pi }{80\\}[/tex]
