Determine whether the statement is true or false. If it

keche0b

keche0b

Answered question

2021-12-07

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Each antiderivative of an nth-degree polynomial function is an (n + 1)th-degree polynomial function

Answer & Explanation

ol3i4c5s4hr

ol3i4c5s4hr

Beginner2021-12-08Added 48 answers

Step 1
Given statement is "Each anti derivative of nth degree polynomial function is a(n+1)th degree polynomial."
Consider a general polynomial f(x)=xn whose degree is n.
Step 2
Then the snit derivative of f(x)=xn is xn+1n+1+C, where C is an arbitrary constant of the integration.
It can be observed that the antiderivative of f(x)=xn is xn+1n+1+C whose derivative is (n+1).
So, each anti derivative of nth degree polynomial function is a(n+1)th degree polynomial.
Thus, the given statement is true.

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