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When we have an equation like
f(x + 7) and we're asked to find the integral, x is really x^1 and its integral is
then x^(1+1) or x^2 ; 7 is really 7x^0 and so the integral is 7x^(0+1) or 7x. The final
(1+1) 2 1
answer being S(x) = x^2 +7x.
2
Integrals (the opposite of derivatives) also raise another question...
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How do we know that
there isn't a constant alone in the integral? The answer is simple. We don't. And so to
account for this, whenever we're solving indefinite integrals, we always end the equation
with "?. + C". So, if we took the indefinite integral of the equation in the previous
paragraph, the actual answer is S(x) = x^2 + 7x +C...
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