Definite integral

1003108104

Level:

Evaluate the integral

\int_{- 2}^{0} (x + 2)^{3} d x

4

28

- 28

12

1003108103

Level:

Evaluate the integral

\int_{- 1}^{1} \frac{x^{2} + 3 x - 10}{x - 2} d x

10

6

8

12

1003108102

Level:

Evaluate the integral

\int_{- 1}^{1} (x^{2} - x) (x + 1) d x

0

\frac{1}{2}

2

1

1003108101

Level:

Evaluate the integral

\int_{1}^{4} \frac{\sqrt{x} - x + x^{2}}{x} d x

6.5

5.5

9.5

14.5

1003118805

Level:

Evaluate the integral

\int_{- 5}^{5} f (x) d x

, where

f (x) = x^{2} + 2

for

x \in [- 5; 1]

and

f (x) = 3

for

x \in [1; 5]

66

\frac{7}{3}

\frac{25}{3}

42

1003118804

Level:

Evaluate the integral

\int_{- 3}^{2} f (x) d x

, where

f (x) = x^{- 4}

for

x \in [- 3; - \frac{1}{2}]

and

f (x) = 12.8 - 6.4 x

for

x \in [- \frac{1}{2}; 2]

. (rounded to

2

decimal places)

22.65

43. \overset{―}{8}

44. \overset{―}{1}

29.7 \overset{―}{1}

1103118803

Level:

The picture shows a graph of a power function

f (x)

. Find the value of the definite integral of this function between

- 1

and

- \frac{1}{2}

1

3

- 1

2

1003118802

Level:

Find positive real numbers

a

and

b

a

b > 0

, such that

b - a = 6

and

\int_{a}^{b} (4 x - 6) d x = 60

a = 1

b = 7

a = 7

b = 1

a = 24

b = 30

a = 1.5

b = 7.5

1003118801

Level:

Which of the following formulas is not equal to

\int_{4}^{8} \frac{3 x + 1}{x^{2} - x - 6} d x

\int_{4}^{8} \frac{2}{x - 3} d x - \int_{4}^{8} \frac{1}{x + 2} d x

\int_{4}^{8} \frac{2}{x - 3} d x + \int_{4}^{8} \frac{1}{x + 2} d x

\int_{4}^{6} \frac{3 x + 1}{x^{2} - x - 6} d x + \int_{6}^{8} \frac{3 x + 1}{x^{2} - 6 - x} d x

\int_{8}^{4} \frac{- 1 - 3 x}{x^{2} - x - 6} d x

1003108008

Level:

Find the value of

p

such that

\int_{- 2}^{3} (3 x^{2} - 5 x^{4} + 4 x + p) d x = - 255.

- 5

5

3

No such

p

exists.

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