Definite integral

1003108007

Level:

What is the difference

I_{1} - I_{2}

, where

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

and

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

4 - \ln 4

\ln 4

4 + \ln 4

\ln 4 - 4

1003108006

Level:

Evaluate the definite integral.

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

\frac{19}{12} + \ln 4

\frac{19}{12} + \ln 2

\frac{43}{12} + \ln 4

\frac{19}{12}

1003108005

Level:

Evaluate the definite integral.

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

- 2 \sqrt{3}

2 \sqrt{3}

0

12 \sqrt{3}

1003108004

Level:

Evaluate the definite integral.

\int_{0}^{1} (6 \sqrt{x} - 5 x^{4} + 3 e^{x}) d x

3 e

6 + 3 e

0

- 3 e

1003108003

Level:

Evaluate the definite integral.

\int_{- \frac{π}{3}}^{\frac{π}{3}} (\sin x - \cos x) d x

- \sqrt{3}

1

1 - \sqrt{3}

1 + \sqrt{3}

1003108002

Level:

Evaluate the definite integral.

\int_{0}^{1} (\frac{5}{3} \cdot \sqrt[3]{x^{2}} - x^{3} + \ln 3) d x

\frac{3}{4} + \ln 3

\frac{5}{4} + \ln 3

\frac{3}{4}

\frac{5}{4}

1003108001

Level:

Evaluate the definite integral.

\int_{1}^{2} (x^{7} - \ln 7 \cdot 7^{x} + 7 x) d x

\frac{3}{8}

- \frac{51}{8}

\frac{51}{8}

\frac{61}{8}

1003027503

Level:

Evaluate the following definite integral.

\int_{e}^{12} \frac{x + 5}{\frac{1}{4} x \cdot (x + 4)} d x

\ln (e + 4) + 5 \ln 12 - 2 \ln 4 - 5

5 + 2 \ln 4 + 5 \ln 12 - \ln (e + 4)

\ln \frac{15}{4} - 5 + \ln (4 + e)

\frac{\ln \frac{12^{5}}{16}}{\ln \frac{e^{5}}{e + 4}}

1003027502

Level:

Evaluate the following definite integral.

\int_{5}^{25} \frac{4 x + 1}{x^{2} - x - 2} d x

\ln \frac{13}{3} + 3 \ln \frac{23}{3}

\ln (26 \cdot 23^{3} \cdot 6 \cdot 3^{3})

\ln \frac{26}{27} + 3 \ln 23 + \ln 6

\ln (24 \cdot 27^{3}) - \ln (4 \cdot 7^{3})

1003027501

Level:

Evaluate the following definite integral.

\int_{e}^{e^{3}} \frac{10 x - 14}{x \cdot (x - 2)} d x

3 \ln \frac{e^{3} - 2}{e - 2} + 14

3 \ln [(e^{3} - 2) (e - 2)] + 14

\ln \frac{e^{3} - 2}{e - 2} + 14

3 \ln (e^{3} - 2) + \ln (e - 2)^{3} + 14

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