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Indefinite Integrals · Question 7 of 90

Question 7

MediumOriginal question

Which of these is an antiderivative of 2xcos⁡(x2)2x\cos(x^2)?

Options for question 7

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. An antiderivative FF is any function with F′(x)F'(x) equal to the given function.

  2. ddxsin⁡(x2)=cos⁡(x2)⋅2x\frac{d}{dx}\sin(x^2) = \cos(x^2) \cdot 2x, which is the given function.

Worth noting

−sin⁡(x2)-\sin(x^2) differentiates to −2xcos⁡(x2)-2x\cos(x^2): the sign is wrong.

Concept
Recognising an antiderivative
Typical time
90 s
Your time
—
The rule this testsIntegration as the reverse of differentiation
Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.

Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.