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Find the area enclosed by the curve y=-x^(2) and the straight line x+y+2=0. |
Answer» ![]() `rArr-x-2=-x^(2)rArrx^(2)-x-2=0` `rArrx^(2)+x-2x-2=0rArrx(x+1)-2(x+1)=0` `rArr(x-2)(x+1)=0rArrx=2, -1` `:. "AREAOF shaded region, " A=abs(int_(-1)^(2)(-x-2+x^(2))dx)=abs(int_(-1)^(2)(x^(2)-x-2)dx)` `=abs([(x^(3))/3-(x^(2))/2-2x]_(-1)^(2))=abs([8/3-4/2-4+1/3+1/2-2])` `=abs((16-12-24++3-12)/6)=abs(-27/6)=9/2" sq units"` |
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