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Evaluate following indefinite integrals.
(a) ∫ 5t 3 -10t -6 + 4 dt
(b) ∫ dy
Solution
There's not whole lot to do here other than use the two formulas. Remember that while integrating powers (which aren't -1 of course) we just add one onto the exponent & then divide through the new exponent.
∫ 5t 3 -10t -6 + 4 dt = 5 ( ¼) t 4 -10 ( 1/-5) t -5 + 4t + c
= 5/4 t 4 + 2t -5 + 4t + c
Be careful while integrating negative exponents. Always remember to add one onto the exponent.
∫ dy = ∫1dy = y + c
In this case we are actually just integrating a one!
It is a fairly short section. It's real purpose is to acknowledge that the exponent properties work for any exponent. We've already used them on integer and rational exponents al
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