if you a a function e.g y=x3+x2+3
the derivative would be y'=3x2+2x
what was done here?
keep co-efficient of x --->multiply coefficient by power if x ----> reduce power by 1 (derivative of constant is 0)
now we have y'=3x2+2x which is the derivative. so how do we go back to the original function? we use intergration which is the reverse of diffrentiation.
what is done?
again keep the co-efficient of x but now go in reverse.
keep coefficient of x ---> increase power by 1 ----> divide coefficient be NEW POWER ---> add a constant k
so integral will be y=3/3x3+2/2x2+k
which simplifies to y=x3+x2+k
Why should we add the coefficinet k? because the derivative of constant is 0 which will not be shown in the derivative so u can't rule out the fact that there is a consanct. to find the constant, you will be given a point on the graph. so for the above example, a point in the graph is (1,5). Replace these values in the integral to find the value of k
5=13+12+k so k=5-2, k=3
we now replace 3 into the integral to get y=x3+x2+3 which is the original equation we stared with.
in general for a function axn, the integral will be axn+1/n+1 + k
