Definite integral | math4u.vsb.cz

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}

.

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

.

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

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}

1003027604

Level:

B

How many times is

\int_{- 3}^{0} \frac{x^{2} + x - 6}{x - 2} d x

smaller than

\int_{4}^{7} \frac{5 x^{2} - 15 x - 20}{x + 1} d x

?

5

times

9

times

they are equal

none of the options

1003027603

Level:

B

How many times is

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{\sin 2 x}{\cos x} d x

bigger than

\int_{- \frac{π}{3}}^{- \frac{π}{6}} \frac{\sin 2 x}{\sin x} d x

?

they are equal

2

times

4

times

none of the options

1003027602

Level:

B

How much smaller is

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

than

\int_{1}^{10} \frac{11 - x}{10} d x

?

more than

1

less than

1

they are equal

cannot be determined

1003027601

Level:

B

How much bigger is

\int_{0}^{3} [(x - 3)^{2} + 1] d x

than

\int_{3}^{6} \log_{5} 5 d x

?

9

15

4

none of the options

9000150401

Level:

A

Evaluate the following definite integral.

\int_{- 3}^{1} (x^{2} + 3 x) d x

- \frac{8}{3}

\frac{8}{3}

- \frac{64}{3}

\frac{64}{3}

9000150402

Level:

A

Evaluate the following definite integral.

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

0

π

2

1

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