I have to find the area between the two curves.y = x^2 and y= x+2 with a lower region of -1 and upper region of 2 ...i know it must be the intergral of the x+2 - intergral of x^2 ...on the calculator it says the area under curve y=x+2 is 7.5 units..and under the x^2 its 3 units....but according to my calculations which i am pretty sure are correct..i end up with a negative when i minus these two which is incorrect so can someone show me the working???
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Let me try my way...
∫-1 -> 2 (x + 2 - x^2) dx
= 1/2 x^2 + 2x - 1/3 x^3 + c | -1 -> 2
= 2 + 4 - 8/3 - (1/2 -2 + 1/3)
= 2 + 4 - 8/3 - 1/2 + 2 - 1/3
= 8 - 9/3 -1/2
= 4 1/2 (unit^2)
(or 4.5 unit^2)
∫-1 -> 2 (x + 2 - x^2) dx
= 1/2 x^2 + 2x - 1/3 x^3 + c | -1 -> 2
= 2 + 4 - 8/3 - (1/2 -2 + 1/3)
= 2 + 4 - 8/3 - 1/2 + 2 - 1/3
= 8 - 9/3 -1/2
= 4 1/2 (unit^2)
(or 4.5 unit^2)