Can I Trust Blind Substitutions in Integration?

[dilan]

I am really new to the calculus field. I have a small problem in integration when it comes to finding the area under a curve when the curve passes beyond the negative side.
Can anyone provide me some links where I can get some good knowledge about integration ?

Thanks

 

[nicktacik]

What's the problem? If you are interested in the net area, then it doesn't matter that the curve is negative. If you are interested in the absolute area, then you break up in the integral into positive and negative parts, and take the absolute value of the negative parts.

 

[premagg]

Never worry during taking the area.Unless otherwise stated just integrate the function within the given limit.If it is stated to say the total absolute area,calculate for +ve and -ve sides separately.

 

[AiRAVATA]

Never worry?

You should always be carefull when it comes to absolute values or substitution methods. What if your substitution is not well defined within the limits of integration, or you have to split the integral into two because of the signs of the integrand?

It's a classic mistake of first year calc students to do substitutions blindly, without concerning what is happening between the domain of integration and the integrand, only to end up with wrong answers.