- #1
vkash
- 318
- 1
There are several rules in calculus which have far reaching applications in field of mathematics, physics etc. unfortunately there is no derivation or visualisation of those rules in my maths book. SO SHAME!.
one of these is that definite integral of function from x1 to x2 gives geometrical area under the curve. There is no well proof of this statement in any book i read. Now I am asking this to you tell me where does it came. why the following statement is true
f(x1)+f(x1+dx)+f(x1+2*dx)+f(x1+3*dx)+...f(x2)=integral from x1 to x2 of function f(x).On more thing is integration by parts this rule is something like this
integral_of {f(x).g(x)}=f(x)* integral_of {g(x)} - integral_of{ (differentiation_of{g(x)} integral_of{f(x)} }.dx
let me say integral_of g(x) = h(x)+C
When we solve any question with help f this rule (ex tan inverse x) then we put integral_of(g(x))= h(x) we simply did not think about C. But why..
these are two basic question i want to ask hope that unlike other places i will get answer here.
one of these is that definite integral of function from x1 to x2 gives geometrical area under the curve. There is no well proof of this statement in any book i read. Now I am asking this to you tell me where does it came. why the following statement is true
f(x1)+f(x1+dx)+f(x1+2*dx)+f(x1+3*dx)+...f(x2)=integral from x1 to x2 of function f(x).On more thing is integration by parts this rule is something like this
integral_of {f(x).g(x)}=f(x)* integral_of {g(x)} - integral_of{ (differentiation_of{g(x)} integral_of{f(x)} }.dx
let me say integral_of g(x) = h(x)+C
When we solve any question with help f this rule (ex tan inverse x) then we put integral_of(g(x))= h(x) we simply did not think about C. But why..
these are two basic question i want to ask hope that unlike other places i will get answer here.