Definite integral

2010001105

Level:

Evaluate the definite integral

\int_{- 1}^{1} (x + 1)^{4} d x

6.4

32

0.2

8

2010001104

Level:

Evaluate the definite integral

\int_{1}^{4} \frac{\sqrt{x} + x^{2} - x^{3}}{x^{2}} d x

- 3.5

- 11

- 5.5

- 3

2010001103

Level:

Evaluate the definite integral.

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

\frac{56}{3} + \ln 27

\frac{56}{3} + \ln 9

\frac{65}{3} + \ln 27

\frac{56}{3}

2010001102

Level:

Evaluate the definite integral.

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

- 2 \sqrt{3}

2 \sqrt{3}

0

12 \sqrt{3}

2010001101

Level:

Evaluate the definite integral.

\int_{0}^{1} (4 \sqrt[3]{x} - 4 x^{3} + 2 e^{x}) d x

2 e

4 + 2 e

0

- 2 e

2000000906

Level:

Evaluate the definite integral

\int_{π}^{2 π} \sin x d x

- 2

- 1

- \frac{π}{2}

0

2000000905

Level:

Evaluate the definite integral

\int_{1}^{2} x d x

\frac{3}{2}

1

6

3

2000000904

Level:

Evaluate the definite integral

\int_{0}^{1} x^{3} d x

\frac{1}{4}

1

\frac{1}{3}

3

2000000903

Level:

Compare definite integrals

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

and

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

I_{1} < I_{2}

I_{1} = I_{2}

I_{1} > I_{2}

These integrals cannot be compared.

2000000902

Level:

Compare definite integrals

I_{1} = \int_{- 10}^{10} x^{4} d x

and

I_{2} = \int_{- 10}^{10} x^{5} d x

I_{1} > I_{2}

I_{1} = I_{2}

I_{1} < I_{2}

These integrals cannot be compared.

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