write a definite integral that represents the area of the region. (Do not evaluate the integral.) 6. y1 = x2 + 2x+1 y2 = 2x +5 6- /2+ -4 -2 + 2 10. y1 = (x - 1)3 12 = 0-1the integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. 12. f [( 3 -2) -3dx 14 . / " ( 2 4 8 - 2 ) dy sketch the region bounded by the graphs of the equations and find the area of the region. 16. y= -x3+2, y=*-3, 2=-1, a=1 18. y= -r'+3x+1, y=->+1 20. f (2) = - 4 3 ' y=0, x=-3, 2=-1 22. f (x) = Vx -1, g(x) =x-1 24. f (y) = y(2 -y), g(y) = -y 26. f (y) = y 9 (y) = 0, y =3 V16 - yz 4 28. g (x) = 2 . y = 4, x=0find the area of the region by integrating a. with respect to x and b. with respect to y . 0. Compare your results. Which method is simpler? In general. will this method always be simpler than the other one? Whyr or why not? 30. y: 32 yzw