Definite integral

2010008005

Level:

Compare the two definite integrals

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

and

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

I_{1} = I_{2}

I_{1} > I_{2}

I_{1} < I_{2}

These integrals cannot be compared.

2010008004

Level:

Compare the two definite integrals

I_{1} = \int_{0}^{1} (x^{6} \cos^{2} x - 20) d x

and

I_{2} = \int_{0}^{1} (20 - x^{6} \cos^{2} x) d x

I_{1} < I_{2}

I_{1} = I_{2}

I_{1} > I_{2}

These integrals cannot be compared.

2010008003

Level:

Compare the two definite integrals

I_{1} = \int_{0}^{1} (10 - x^{4} \sin^{2} x) d x

and

I_{2} = \int_{0}^{1} (x^{4} \sin^{2} x - 10) d x

I_{1} > I_{2}

I_{1} = I_{2}

I_{1} < I_{2}

These integrals cannot be compared.

2010008002

Level:

Compare the two definite integrals

I_{1} = \int_{0}^{3} \frac{x^{3}}{3^{x}} d x

and

I_{2} = \int_{3}^{0} \frac{x^{3}}{3^{x}} d x

I_{1} > I_{2}

I_{1} = I_{2}

I_{1} < I_{2}

These integrals cannot be compared.

2010008001

Level:

Compare the two definite integrals

I_{1} = \int_{0}^{2} x^{5} \cdot 2^{x} d x

and

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

I_{1} > I_{2}

I_{1} = I_{2}

I_{1} < I_{2}

These integrals cannot be compared.

2010001204

Level:

Evaluate the definite integral.

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

\ln \frac{5}{8}

\ln 40

\ln \frac{8}{5}

- \ln 40

2010001203

Level:

Evaluate the definite integral.

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

\ln 2

\ln 1

\ln 8

3 \ln 8

2010001202

Level:

Evaluate the definite integral.

\int_{- π}^{\frac{π}{2}} x \cdot \cos x d x

\frac{π + 2}{2}

π + 1

\frac{π}{2}

\frac{π}{2} - 1

2010001201

Level:

Evaluate the definite integral

\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{cotg b}{\sin 2 b} d b

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

- 2 \sqrt{3}

2 \sqrt{3}

- \sqrt{3}

2010001106

Level:

Evaluate the definite integral

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

1 + \ln 8

- 2 + \ln 8

1 + \ln {(\frac{3}{2})}^{3}

1 + (\ln 2)^{3}

« first
‹ previous
1
2
3
4
5
6
7
8
9
…
next ›
last »

2010008005

2010008004

2010008003

2010008002

2010008001

2010001204

2010001203

2010001202

2010001201

2010001106

Events

Akce

Interests

Zajímavosti

About portal

O portálu