Question

Questions concerning integration.
1. When we differentiate an equation, we can find a point. What about when we integrate an equation? What are we finding?

2. When we differentiate an equation, we take limit (x->0). I understand this part. But why are we taking limit (x->∞) for integration?

PS: FYI, I'm not doing my homework/test/exam, I'm just revising what I've learnt.

Answer 1

answer to ur first question:
graphically, differentiation gives us the 'slope' of the tangent at any point on the curve.
while, integration gives us the 'area' under the curve.

(pardon the shabby drawing!)
here, integration will give u the area of the shaded region. and differentiation will give u the slope of the dark line.
hope i got the point across...

Answer 2

What about for indefinite integrals? What are we finding?

Answer 3

in the above graph, if i had not defined the the region whose area i want to find (by drawing that vertical line) then i would be finding the area under the whole curve...not just a part of it (as i did here). 'indefinite' means that u don't have a defined region/interval in which u're supposed to integrate. so u'll end up integrating the entire curve --> finding the area under the entire curve.

Answer 4

So, for the first question:
Differentiation is to find a slope of the equation.
Integration is to find the area under the curve.
Right?

Answer 5

yup.

Answer 6

Thanks!
What about for the second question?

Answer 7

i'm sorry i can't help with the second question. maybe @mukushla can.

Answer 8

''we taking limit (x->∞) for integration''

can u plz show it with an example..

Answer 9

or if u read that somewhere, then post the that para here. so that we can relate to it.

Answer 10

\[\int_a^b f(x)dx = \lim_{n \rightarrow \infty} \sum_{i=1}^{n}f(z_i)\Delta x\]