An indefinite integral yields an equation. A definite integral yeilds a number.
When dealing with a definite integral, we don't care about the + C. It's completely irrelevant:
My first post(question) here.
what is indefinite integral,is integral without limits called as indefintie integral?
and my teacher said that for definite integral the variable of integration could be anything .I understand this since it will read the same result.
But is this not possible for indefinite integral?
If you change C, you change the function. and may have the same derivative, but for all x, the two functions are completely different. Your constant of integration is just that; a constant. Constants in no way affect your derivative and so your +C can be anything from to .
We don't always take the integral from b to a. That's only when we're finding accumulated area, in which case the +C is negligable. But sometimes we just want F(a) or F(b), in which case it's very important to know.
Say we know the antiderivative of is . And say we know that . This gives us a point on the function with which to calculate C. We know that , so C must equal 1.
It is common to write where the variable is shown in the upper limit so that the "dummy variable" inside the integral really is "dummy".
Actually what i wanted to ask (say) in your example,how would anything change if i change the variable to u and integrate and subtitute again the original variable (say x) as HallsofIvy has done.
Thank you vary much once again