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Answer :
The antiderivative of the function f(x) = 21x^(2) + 12x -5 is F(x) = 7x^(3) + 6x^(2) - 5x + C, where C is the constant of integration.
The subject of the question is related to calculus in Mathematics, specifically about finding the antiderivative of a given function. The function given seems a little jumbled, but the first one listed, f(x) = 21x^(2) + 12x - 5, is clear.
To find the antiderivative, we use the power rule for integration which states that the integral of x^n dx is (1/(n+1))*x^(n+1). Applying this rule to each term:
The antiderivative of 21x^(2) is (21/3)*x^(3) = 7x^(3)
The antiderivative of 12x is (12/2)*x^(2) = 6x^(2)
The antiderivative of -5 is -5x
So the antiderivative of the function f(x) = 21x^(2) + 12x - 5 is F(x) = 7x^(3) + 6x^(2) - 5x + C, where C is the constant of integration.
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