What is integration?
Integration is the reverse of calculating the derivative in maths. We can use integration to determine the area under a graph between to x values. I will demonstrate a basic integration question to show you. Simply, when terms needed to be integrated are being added and subtracted from one another, we can deal with them separately. For example, find the integral of the polynomial S -x3 + 8x2 - 4x +3 dx. The power rule is that the integral of Sxndx = xn+1 /(n+1) + C when n isn't equal to 1. Furthermore, S t dx = tx+C. Knowing this we get -x4 /4 + 8x3 / 3 - 4x2 /2 + 3x + C which is equivalent to -x4 /4 + 8x3 / 3 - 2x2 + 3x + C. We can check this by differentiating the solution to see if it matches the initial polynomial. When we think of integration as reverse differentiation, when differentiating all number terms go to zero, when we integrate we need to account for this missing term, therefore the +C is needed to represent all possible terms that this could be.
