Free Printable 微積分

1.

試求不定積分 $\int_{ }^{ }4dx$ =

a)

4

b)

4x

c)

4x+c

d)

$2x^2+c$

2.

試求不定積分 $\int_{ }^{ }2xdx=$

a)

2

b)

2x

c)

2x+c

d)

$x^2+c$

3.

試求不定積分 $\int_{ }^{ }3x^2dx=$

a)

$x^3+c$

b)

$x^3+2$

c)

$x^3$

d)

$3x^2+c$

4.

$\int_0^52dx=$

a)

5

b)

10

c)

15

d)

20

5.

$\int_0^42dx=$

a)

8

b)

16

c)

32

d)

40

6.

試求不定積分 $\int_{ }^{ }x^3dx=$

a)

$x^3$

b)

$x^4+2$

c)

$\frac{1}{4}x^4$

d)

$\frac{1}{4}x^4+c$

7.

試求不定積分 $\int_{ }^{ }x^5dx=$

a)

$\frac{1}{6}x^6$

b)

$x^6$

c)

$\frac{1}{3}x^6$

d)

$\frac{1}{6}x^6+c$

8.

試求不定積分 $\int_{ }^{ }\left(3x^2-2\right)dx=$

a)

$x^3$

b)

$x^3+2x$

c)

$x^3-2x+c$

d)

$x^4+c$

9.

試求不定積分 $\int_1^2x^3dx=$

a)

$\frac{15}{4}$

b)

$\frac{17}{5}$

c)

$\frac{16}{3}$

d)

6

10.

試求不定積分 $\int_{ }^{ }x^{\frac{4}{3}}dx=$

a)

$x^{\frac{3}{7}}$

b)

$x^{\frac{7}{3}}$

c)

$x^{\frac{7}{3}}+c$

d)

$\frac{3}{7}x^{\frac{7}{3}}+c$

11.

試求不定積分 $\int_{ }^{ }x\left(2-x\right)dx=$

a)

$-\frac{1}{3}x^3+x^2$

b)

- $-\frac{1}{3}x^3+x^2+c$

c)

$x^4+c$

d)

$x^3-2x+c$

12.

$\int_{ }^{ }\ \frac{2}{x^5}dx=$

a)

$2x^4+c$

b)

$2x^4$

c)

$-\frac{1}{2x^4}+c$

d)

$-\frac{1}{2x^4}$

13.

試求不定積分 $\int_{ }^{ }6\left(x+2\right)^5dx=$

a)

$x^6$

b)

$\left(x+2\right)^6$

c)

$\left(x+2\right)^6+c$

d)

$x^6+c$

14.

已知 $\int_0^3f\left(x\right)dx=5，\ \int_3^6f\left(x\right)dx=2，\int_0^66f\left(x\right)dx=?$

a)

7

b)

14

c)

35

d)

42

15.

$\int_{ }^{ }\left(x+3\right)^2dx-\int_{ }^{ }\left(x+2\right)^2dx=$

a)

$x^2+3x+c$

b)

$x^2+4x+c$

c)

$x^2+5x+c$

d)

$x^2+6x+c$

16.

$\int_1^3\left(x^2+4x^3-1\right)dx=$

a)

$\frac{150}{7}$

b)

$\frac{260}{3}$

c)

$\frac{119}{5}$

d)

$\frac{211}{2}$

17.

$\int_1^2f\left(x\right)dx=12，\int_2^6f\left(x\right)dx=-5，\int_1^2g\left(x\right)dx=-8，\int_2^6g\left(x\right)dx=4，find\ \int_1^6\left[4f\left(x\right)-g\left(x\right)\right]dx=?$

a)

28

b)

32

c)

34

d)

42

18.

試求無窮等比級數 $1+\frac{1}{3}+\left(\frac{1}{3}\right)^2\ +\left(\frac{1}{3}\right)^3\ \ +...=?\ Hint\ \ \frac{a}{1-r}$

a)

$\frac{4}{3}$

b)

$\frac{3}{2}$

c)

$\frac{5}{4}$

d)

$\frac{6}{5}$

19.

試將 $0.\overline{5}$ 化為最簡分數為

a)

$\frac{5}{9}$

b)

$\frac{5}{11}$

c)

$\frac{13}{5}$

d)

$\frac{17}{5}$

20.

試求定積分 $\int_1^3x^2dx=?$

a)

$\frac{20}{3}$

b)

$\frac{26}{3}$

c)

$\frac{28}{3}$

d)

$\frac{29}{3}$

微積分_0605

Total questions: 20

Worksheet time: 2hrs 40mins

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