Integrate the following equation to find y: dy/dx = 3x^2 + 2x + 6
Notice that integration is simply the opposite of differentiation. So, if we just integrate this term-by-term then we can find an expression of y in terms of x.
So, when we integrate dy/dx becomes y.
Integrating 3x^2, we add 1 to the power and divide the coefficient by this new power. So we will get 3x^3/3 which is the same as x^3.
Then, by the same process, integrating 2x will give 2x^2/2 which is equal to x^2.
Now, if we think of 6 as the same as 6x^0 (since anything ^0 equals 1) then by the same process we get 6x^1/1 which is just 6x.
Finally, we must remember that we cannot find any term which are just a constant as they would have disappeared when y was differentiated, so we must add a +c to the end.
Bringing this all together, we get y=x^3+x^2+6x+c
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