these are small doubts that stopped me proceeding further
1) when we integerate a odd or differentiate a odd function should we get a even function and vice versa
for eg-integeral sinx=-cosx
d(sinx)/dx=cosx
here sinx is an odd function and while both integrating and differentiating we get an even function cosx
2) what should we do if we have to area under the curve if it involves points of inflection should we seperately integerateeach of them and add their modulii or as usual integerate between the upper and lower limits
3) what are the general procedure to follow when asum invoves modulus function and greatest integer function something like squaring or sandwiching principle
thats all for this one please answer these
to manish sir
Let us discuss this point by point:
- It is true for differentiation. However, integration invloves a constant as well. Do you think a fuction of the form f(x) + C can be even or odd in general?
- Point of inflextion only means that the change in the function is extremely gradual. However, in integration all we are interested in is the continuity of the function and not how it changes. I do not think this will change the way how we can approach a problem. In case you have come across a particular case, you can post it here.
- It depends on the problem. However, in case of greatest integer function, the general method is to remove that function. This removal is done by replacing it with an integer depending upon the limits given. It is common to use sandwitch theorem if the problem belongs to, "limit" chapter. Modulus function is also removed by generally considering two cases, viz Undetermined error: @@x>=0@@ and x < 0.