Hi all, just wondering if someone could explain to me about define integrals.(adsbygoogle = window.adsbygoogle || []).push({});

Say i have F(x)=0.5x^{2}-2 and F(x)=x^{3}+x^{2}-6x and i want to find the area of the regions which is satisfied from -2 to 2.

so [tex]\int[/tex]0.5x^{2}-2 from -2 to 2. [tex]\int[/tex]x^{3}+x^{2}-6x from -2 to 2.

Now with the cubic, from -2 to 0 is supposedly positive and from 0 to 2 it's negative, is that true i thought the it doesn't matter which region the area is in it'll always be counted as positive.

so, [tex]\int[/tex]x^{3}+x^{2}-6x from -2 to 0. = [tex]\int[/tex](-2)^{3}+(-2)^{2}-6(-2) - [tex]\int[/tex](0)^{3}+(0)^{2}-6(0) = 8-0 = 8units^{2}

[tex]\int[/tex]x^{3}+x^{2}-6x from 0 to 2. = [tex]\int[/tex](0)^{3}+(0)^{2}-6(0) - [tex]\int[/tex](2)^{3}+(2)^{2}-6(2) = 0- 0 = 0 units^{2}

Therefore, Area from (-2 to 0)+ Area from (0 to 2) = 8+0 = 8units^{2}

But using my calculator doing the same steps (except in the graphing section) doing -2 to 0 and adding it to 0 to 2's value i get 16units^{2}( 10.667+5.333)

I don't know whats going on..

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# Definite Integrals

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