The base of a solid in the region bounded by the parabola x2 + y = 4 and the line x + y = 2. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid?

Answer:volume of the solid is 3.180Step-by-step explanation:given dataline x + y = 2parabola  x2 + y = 4to find out the volume of the solidsolutionwe draw a graph between line and parabola as show in fig given below attachline 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 ) /2we 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 / 20volume of the solid is 3.180