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Indefinite Integrals · Question 2 of 90

Question 2

EasyOriginal question

If F′(x)=3x2F'(x) = 3x^2 and F(1)=4F(1) = 4, what is F(x)F(x)?

Options for question 2

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. F(x)=∫3x2 dx=x3+CF(x) = \int 3x^2\,dx = x^3 + C.

  2. F(1)=1+C=4F(1) = 1 + C = 4 gives C=3C = 3, so F(x)=x3+3F(x) = x^3 + 3.

Worth noting

x3+4x^3 + 4 gives F(1)=5F(1) = 5: the 4 is the value at 1, not the constant.

Concept
Fixing the constant of integration
Typical time
60 s
Your time
—
The rule this testsIntegration as the reverse of differentiation
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