When you integrate a function why do you add a constant?
That is a good question. Let me try to help you figure this out by working through a few simple examples. We know that differentiation is like a reverse process of right? So let us differentiate a few functions.
What is the derivative of f(x) = x^2 , f'(x)=2x ,right?
What is the derivative of f(x) = x^2 + 5, also f'(x)=2x, right?
What is the derivative of f(x) = x^2 + 10, also f'(x)=2x, right?
As you see the derivative is the same for all the function above. This is because differentiation gets rid of any constant given, meaning any value with no power of x in front of it disappears. Therefore, we add a constant when we integrate as we do not know what the exact function is, we just know what the coefficients of x are. Here is are diagrams to help understand this.
Related Maths A Level answers
All answers ▸Find the coordinates of the stationary points for the curve y = x^4 - 2*x^2 + 5.
What is the indefinite integral of xlog(x)?
Find the exact solution, in its simplest form, to the equation ln(4y + 7) = 3 + ln(2 – y) (Core Maths 3 Style Question)
Find the exact value of x from the equation 3^x * e^4x = e^7