Antiderivatives and Indefinite Integrals Practice

Sample questions

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1. Sample 1difficulty 1/5

   $\int 6 x^5\,dx =$

   • A

     $x^6/6 + C$

   • B

     $6 x^6 + C$

   • C

     $30 x^4 + C$

   • D

     $x^6 + C$

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   Why

   $6 \cdot x^6/6 = x^6$.

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2. Sample 2difficulty 1/5

   $\displaystyle\int x^3\,dx =$

   • A

     $\dfrac{x^4}{4} + C$

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   • B

     $\dfrac{x^3}{3} + C$

   • C

     $3x^2 + C$

   • D

     $x^4 + C$

   Why

   Power rule for integrals: $\int x^n\,dx = x^{n+1}/(n+1) + C$.

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3. Sample 3difficulty 1/5

   $\displaystyle\int \sin x\,dx =$

   • A

     $\cos x + C$

   • B

     $\sin x + C$

   • C

     $-\cos x + C$

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   • D

     $-\sin x + C$

   Why

   Antiderivative of $\sin$ is $-\cos$.

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4. Sample 4difficulty 1/5

   $\displaystyle\int \cos x\,dx =$

   • A

     $\sin x + C$

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   • B

     $-\cos x + C$

   • C

     $\cos x + C$

   • D

     $-\sin x + C$

   Why

   Antiderivative.

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5. Sample 5difficulty 1/5

   $\displaystyle\int 5\,dx =$

   • A

     $0$

   • B

     $5$

   • C

     $x^5 + C$

   • D

     $5x + C$

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   Why

   $\int k\,dx = kx + C$.

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