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How do you find the antiderivative of #3t^2+1#?

Answer 1

Ezekiel Alexander

#t^3+t+c#

#"integrate each term using the "color(blue)"power rule"#

#•int(ax^n)=a/(n+1)x^(n+1);n!=-1#

#rArrint(3t^2+1)dt#

#=3/3t^3+t+c=t^3+t+c#

#"where c is the constant of integration"#

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Answer 2

Charles Arocha

To find the antiderivative of (3t^2 + 1), you integrate each term separately. The antiderivative of (3t^2) is (\frac{3}{3} t^3 = t^3), and the antiderivative of (1) is (t). So, the antiderivative of (3t^2 + 1) is (t^3 + t + C), where (C) is the constant of integration.

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Answer 3

Isabella Ackerman

The antiderivative of (3t^2 + 1) with respect to (t) is (\frac{t^3}{1} + t + C), where (C) is the constant of integration. So, the antiderivative is ( \frac{t^3}{3} + t + C ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.