Question

this is a question from my Calculus class can you explain it for me?

"We know that an indefinite integral leaves us with a + C at the end. Discuss what this is all about and give an example of a real life situation where the + C is important."

Answer 1

We know that integration is the process that is reverse of differentiation. And as differentiation of constant function is zero that's why we use +C in indefinate integral to represent the constant value.

Example is real life is,

Suppose a man velocity is given by v(t) = t m/s and we have to calculate the total distance covered by man given that at t = 0 the distance covered by the man is 10m.

So for this case the distance travelled will be integration of v(t) with respect to t that is s(t) = t^2/2 + C and since at t = 0 s(0) = 10 = C.

So s(t) = t^2/2 +10 .

In this way +C is used in real life.

Thank You.

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