FTC and Definite Integrals Practice

Sample questions

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1. Sample 1difficulty 1/5

   $\displaystyle\int_b^a f(x)\,dx =$

   • A

     $-\int_a^b f(x)\,dx$

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   • B

     $\int_a^b f(x)\,dx$

   • C

     $0$

   • D

     $f(b) - f(a)$

   Why

   Reversing the limits negates the integral.

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2. Sample 2difficulty 1/5

   $\displaystyle\int_0^2 x\,dx =$

   • A

     $4$

   • B

     $2$

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   • C

     $3$

   • D

     $1$

   Why

   $[x^2/2]_0^2 = 2$.

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3. Sample 3difficulty 1/5

   $\displaystyle\int_0^1 (3 f(x) + 2 g(x))\,dx$ if $\int_0^1 f = 4$ and $\int_0^1 g = -1$ equals

   • A

     $10$

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   • B

     $14$

   • C

     $3$

   • D

     $11$

   Why

   $3(4) + 2(-1) = 12 - 2 = 10$.

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4. Sample 4difficulty 1/5

   $\displaystyle\int_0^1 e^x\,dx =$

   • A

     $e - 1$

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   • B

     $1$

   • C

     $0$

   • D

     $e$

   Why

   $[e^x]_0^1 = e - 1$.

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5. Sample 5difficulty 2/5

   $\displaystyle\int_1^2 \dfrac{1}{x^2}\,dx =$

   • A

     $2$

   • B

     $1$

   • C

     $\tfrac{1}{2}$

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   • D

     $\tfrac{3}{2}$

   Why

   $[-1/x]_1^2 = -1/2 - (-1) = 1/2$.

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