When integrating, why do we add a constant to the resulting equation?
The +c is to represent the loss in information after differentiation. Remember, integration is just the reverse of differentiation. Say we had this function:
f(x) = 2x^2 + 1 And we differentiate: f'(x) = 4x
Now take this second function: g(x) = 2x^2 + 4 And differentiating gives us: g'(x) = 4x
We can see that g'(x) = f'(x). So, if we try and integrate 4x, what do we get? Would it be 2x^2 + 1, or 2x^2 + 4?
The answer is it could be either. Or 2x^2 + 3. Or 2x^2 + 109823.1203981! There are infinite solutions to integration, depending on how you got there from differentiating. That's why we add the +c - to represent all the different possibilities.
TC
Related Maths A Level answers
All answers ▸two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u
Differentiate sin(x^3) with respect to y
A curve has the equation: x^3 - x - y^3 - 20 = 0. Find dy/dx in terms of x and y.
Why is it that the sum of all natural numbers up to n is 1/2(n)(n+1)?