Definite integral | math4u.vsb.cz

1003027701

Level:

A

How much bigger is

\int_{0}^{π} (x + \sin x) d x

than

\int_{1}^{π} x d x

?

\frac{5}{2}

0.5

π - 1

\frac{3}{2}

1003027702

Level:

A

How much smaller is

\int_{- \frac{π}{2}}^{\frac{π}{2}} \sin x d x

than

\int_{0}^{π} (\cos x + 1) d x

?

π

1 - π

π - 1

2 π

1003027703

Level:

A

Compare two definite integrals

I_{1} = \int_{0}^{\frac{π}{2}} \cos x d x

and

I_{2} = \int_{0}^{2 π} 2 \cos x d x

.

I_{1}

is bigger than

I_{2}

by

1

.

I_{1}

is smaller than

I_{2}

by

1

.

I_{1}

is equal to

I_{2}

.

I_{1}

is smaller than

I_{2}

by

2

.

1003027704

Level:

A

Compare two definite integrals

I_{1} = \int_{- 1}^{1} x^{8} d x

and

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

.

I_{2}

is bigger than

I_{1}

by

\frac{4}{9}

.

I_{1}

is bigger than

I_{2}

by

\frac{4}{9}

.

I_{2}

is bigger than

I_{1}

by

\frac{2}{9}

.

I_{1}

is bigger than

I_{2}

by

\frac{2}{9}

.

1003027705

Level:

A

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}

1003027706

Level:

A

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}

6

\frac{π}{6}

1003027707

Level:

A

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

1003027708

Level:

A

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

1003027709

Level:

A

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

1003027710

Level:

A

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

1
2
3
4
5
6
7
8
9
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