Question

Find the area bounded by the graphs ? = −3? 2 ??? ? = −27. Hint: sketch the functions and find their point of intersection.

Answer 1

Solution Step I the curves) + Given curves are y=-343 17=-27 ( Find point of integration of both y=-3x² and y=-27 → -3702=-27 » x²= 9 When x= -3, y = -27 x= 3; y = -27 so point of interesection are 73,27) ,(3,-27)

Stcp 2 (Plot both cweves.) y=-27 27 | 18+ 3x^ -3 2= 3 . 1631-27). *327777 .. 2=3 Hore shaded Region R is the region of integuation Step? (choose limits of the integual :) By looking at the vertical streep drawn inside R we cars.se y varies from .-27 - to -3x2 and a varies from 3 to 3. so . -27<4 <-3x² 36223 stepy (Evaluate the integral) . . (A) Area = lsayda & J ayda 3 -3x? 3 7-372 Aalmon az U ل 32 - 3 سالن :73 - *43**+27) dx = -faadu +321da > A-- 3 + [27272 A--[7-(-27)] + [81-481)] A = -554] + [162] A= 108] . Hence. Area is 108 unit? :