Definite integral

Volume of a Solid

Submitted by robert.marik on Sun, 11/25/2018 - 01:43

1003108205

Level:

Compare the two definite integrals

I_{1} = \int_{- 1}^{1} (x + \frac{π}{2}) d x

and

I_{2} = \int_{0}^{\frac{π}{4}} tg x \cdot \cos x d x

I_{1}

is bigger than

I_{2}

I_{1}

is smaller than

I_{2}

I_{1}

is equal to

I_{2}

These integrals cannot be compared.

1003108204

Level:

The value of the definite integral

\int_{- \frac{π}{4}}^{\frac{π}{4}} ({tg}^{2} x + 1) d x

is:

a whole number

a decimal number

a proper fraction

an irrational number

1003108203

Level:

Compare the definite integral

I = \int_{0}^{\frac{π}{4}} \frac{\cos 2 b}{\cos^{2} b} d b

to the number

\frac{π}{2}

I

is smaller than

\frac{π}{2}

1

I

is bigger than

\frac{π}{2}

1

I

is equal to

\frac{π}{2}

I

is smaller than

\frac{π}{2}

\frac{π}{4}

1003108202

Level:

Evaluate the definite integral

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{tg a}{\sin 2 a} d a

\frac{\sqrt{3}}{3}

\frac{2 \sqrt{3}}{3}

- \frac{2 \sqrt{3}}{3}

- \frac{\sqrt{3}}{3}

1003108201

Level:

Evaluate the definite integral

\int_{0}^{\frac{π}{6}} \frac{3 \cos 2 t}{\cos t + \sin t} d t

. Which of the following intervals contains the value of the integral?

(0.8; 1.2)

(0.4; 0.8)

(- 0.8; - 0.1)

(- 0.1; 0.4)

1003108108

Level:

Compare the value of

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

to the number

\frac{4}{15}

It is bigger than

\frac{4}{15}

It is smaller than

\frac{4}{15}

It equals

\frac{4}{15}

It cannot be compared.

1003108107

Level:

Compare the value of

\int_{1}^{2} \frac{x^{2} \cdot \sqrt[3]{x}}{\sqrt[4]{x^{3}}} d x

to zero.

It is bigger than

0

It is smaller than

0

It equals

0

It cannot be compared.

1003108106

Level:

How many times is

\int_{0}^{\frac{π}{2}} 3 \cos x d x

bigger than

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

6

times

3

times

2

times

It is not bigger.

1003108105

Level:

Evaluate the integral

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

1 + \ln {(\frac{3}{4})}^{4}

1 - 4 \ln 12

4 \ln 0.75

4 \ln 12

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