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Antiderivatives and Indefinite Integrals

AP Calculus AB· difficulty 2/5

Find ff given f′(x)=2xf'(x) = 2x and f(1)=5f(1) = 5.

  • A

    f(x)=x2+5f(x) = x^2 + 5

  • B

    f(x)=x2+4f(x) = x^2 + 4

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  • C

    f(x)=2x+3f(x) = 2x + 3

  • D

    f(x)=x2f(x) = x^2

Explanation

f(x)=x2+Cf(x) = x^2 + C. f(1)=1+C=5⇒C=4f(1) = 1 + C = 5 \Rightarrow C = 4.

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