Question

Find the area of the region bounded between the curves y = x and y = 2 – x2 by: a. Integrating with respect to x Integrating with respect to y

Answer 1

Y=x : Cir) And untersection points : set X22-2 ya 2-x2 + (x+2)(x-1)=0 + X2-2 or x= 1 ☺ integrating with respect to x axis (-2,-2) Area = 5(2-x2)-x dx = 5-<3x+2dx -*- *+2x)'= (1+)-(4-2-4) = 4.5 (2) integrating with respect to y-axis y - 2-x24 X2-2-4 = = 12-y

16012) - - - C ) : To the left of the graphs You x=f2-4 Area = f 4-612-9) dy y=-2 t y=1 1-272) I + sasa-y dy = $ y + vary dy + saday day - [92]}+{@y)*743) + Ye_95%d), -(-4) - (4°) - 1 (0-1) =(-3) -869) +++ - + 6 = 4.5