Definite integral

2000000901

Level:

Compare definite integrals

I_{1} = \int_{0}^{\frac{π}{4}} tg x d x

and

I_{2} = \int_{\frac{π}{4}}^{\frac{π}{2}} cotg x d x

I_{1} = I_{2}

I_{1} > I_{2}

I_{1} < I_{2}

These integrals cannot be compared.

2010000003

Level:

Evaluate the definite integral.

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

1

\sqrt{3}

1 + \sqrt{3}

0

2010000002

Level:

Evaluate the definite integral.

\int_{0}^{1} (\ln 5 - \frac{7}{5} \sqrt[5]{x^{2}} + x^{4}) d x

\ln 5 - \frac{4}{5}

\ln 5 - \frac{1}{5}

- \frac{4}{5}

- \frac{1}{5}

2010000001

Level:

Vypočítejte určitý integrál.

\int_{1}^{2} (5^{x} \cdot \ln 5 - x^{5} - 4 x) d x

\frac{7}{2}

- \frac{5}{2}

- \frac{1}{2}

- \frac{5}{6}

Equations with Definite Integral

Submitted by ladislav.foltyn on Fri, 05/31/2019 - 13:04

Question:

Choose the correct value of the unknown positive real number

m

, so that the given equality holds.

Submitted by ladislav.foltyn on Thu, 05/23/2019 - 11:48

Question:

Choose the correct value of the definite integral:

1003124304

Level:

Given a function

f (x) = a x^{4} + b x

, find real numbers

a

and

b

, such that

\int_{0}^{1} f (x) d x = 27

and

\int_{- 1}^{0} f (x) d x = 57

a = 210

b = - 30

a = 210

b = 30

a = 75

b = 60

a = 30

b = 210

1003124308

Level:

Which of the values of a real number

a \in (π; 2 π)

makes the equality

\int_{π}^{a + π} \sin 2 x d x = 1

true?

a = \frac{3}{2} π

a = \frac{3}{4} π

a = \frac{1}{2} π

a = \frac{2}{3} π

1003124307

Level:

Which of the positive values of a real number

a

makes the equality

\int_{a}^{7} \frac{6 x - 5}{3 x^{2} - 5 x} d x = \ln 56

true?

a = 2

a = 1

a = 3

a = 5

1003124306

Level:

Which of the positive values of a real number

a

makes the equality

\int_{1}^{a} \frac{3}{3 x + 5} d x = \ln \frac{7}{4}

true?

a = 3

a = 2

a = 4

a = 5

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Definite integral

2000000901

2010000003

2010000002

2010000001

Equations with Definite Integral