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ok, my question involves two different sets of directions ..

1. Use integration to find the area of each shaded region.

2. Evaluate each definite integral.

Ok, my question is this... do i do the same thing for both of these directions? ..

Even further... say I have a function that goes over and under the x-axis.. and i'm asked to find the area when the function is bounded in such a way that the area would be both over and under the x-axis... For direction #1, i would find the zeros of the function and use the fundamental theorem of calculus and do each part separately.. taking the absolute value of each.. and adding the two areas together.. ok.. i got that.. but for #2.. do i do the same thing? or would i just apply the fundamental theorem of calculus without absolute values and without finding zeros?

A good example would be:

http://img400.imageshack.us/img400/6026/integralquestion7ht.gif [Broken]

Is this done correctly? or would i still do any absolute value or splitting into regions with direction #2?

If i'm correct.. Direction #2 can have negative values or even 0, and direction #1 will always have positive values?

Please clarify all this someone.. thanks.

1. Use integration to find the area of each shaded region.

2. Evaluate each definite integral.

Ok, my question is this... do i do the same thing for both of these directions? ..

Even further... say I have a function that goes over and under the x-axis.. and i'm asked to find the area when the function is bounded in such a way that the area would be both over and under the x-axis... For direction #1, i would find the zeros of the function and use the fundamental theorem of calculus and do each part separately.. taking the absolute value of each.. and adding the two areas together.. ok.. i got that.. but for #2.. do i do the same thing? or would i just apply the fundamental theorem of calculus without absolute values and without finding zeros?

A good example would be:

http://img400.imageshack.us/img400/6026/integralquestion7ht.gif [Broken]

Is this done correctly? or would i still do any absolute value or splitting into regions with direction #2?

If i'm correct.. Direction #2 can have negative values or even 0, and direction #1 will always have positive values?

Please clarify all this someone.. thanks.

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