Definite integral

1003027714

Level:

Which of the given values of

a

makes the statement true?

\int_{0}^{1} x^{8} d x = a \cdot \int_{- 1}^{0} x^{24} d x

a = 2. \overset{―}{7}

a = 3

a = 0.36

a = 16

1003027713

Level:

Which of the given values of

a

makes the statement true?

a \cdot \int_{0}^{\frac{π}{2}} \cos x d x = \int_{2 π}^{3 π} \sin x d x

a = 2

a = π

a = 4

a = 1

1003027712

Level:

Compare two definite integrals

I_{1} = \int_{1}^{2} \frac{1}{x} d x

and

I_{2} = \int_{2}^{4} \frac{1}{x} d x

I_{1}

is equal to

I_{2}

I_{2}

is twice as big as

I_{1}

I_{1}

is twice as big as

I_{2}

I_{1}

4

times as big as

I_{2}

1003027711

Level:

Compare two definite integrals

I_{1} = \int_{0}^{5} 0.6 x d x

and

I_{2} = \int_{0}^{5} 1.8 x d x

I_{2}

3

times as big as

I_{1}

I_{1}

3

times as big as

I_{2}

I_{2}

1.2

multiple of

I_{1}

I_{2}

30

times as big as

I_{1}

1003027710

Level:

How many times bigger is

\int_{0}^{4} (3 x + 3) d x

than

\int_{2}^{3} (3 x - 6) d x

24

times

6

times

9

times

54

times

1003027709

Level:

How many times bigger is

\int_{0}^{7} (- \frac{4}{7} x + 4) d x

than

\int_{- 1}^{0} (- \frac{4}{3} x + \frac{4}{3}) d x

7

times

6

times

14

times

2

times

1003027708

Level:

How many times bigger is

\int_{5}^{10} (1.2 x - 6) d x

than

\int_{0}^{5} 0.4 x d x

3

times

2

times

4

times

7

times

1003027707

Level:

Which of the given values of

a

makes the statement true?

\int_{0}^{5} 1.6 x d x - a = \int_{0}^{5} 0.6 x d x

a = 12.5

a = 1

a = 13.5

a = 8

1003027706

Level:

How much smaller is

\int_{\frac{5 π}{6}}^{π} 3 \sin x d x

than

\int_{0}^{\frac{5 π}{6}} 3 \sin x d x

3 \sqrt{3}

3 \sqrt{2}

\frac{π}{6}

1003027705

Level:

How much smaller is

\int_{0}^{1} x^{15} d x

than

\int_{0}^{1} x^{5} d x

\frac{5}{48}

\frac{11}{48}

\frac{5}{32}

\frac{11}{32}

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