Definite integral

2000000901

Level:

Compare definite integrals $I_1 = \int\limits_0^{\frac{\pi}{4}}\mathrm{tg}\,x \,\mathrm{d}x$ and $I_2= \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}}\mathrm{cotg}\, x\,\mathrm{d}x$.

$I_1=I_2$

$I_1 > I_2$

$I_1 < I_2$

These integrals cannot be compared.

2010000003

Level:

Evaluate the definite integral. \[ \int\limits_{-\frac{\pi}6}^{\frac{\pi}6}(\cos ⁡x-\sin ⁡x )\,\mathrm{d}x \]

$ 1 $

$ \sqrt3 $

$ 1+\sqrt3 $

$0$

2010000002

Level:

Evaluate the definite integral. \[ \int\limits_0^1\left(\ln5 - \frac{7}{5}\sqrt[5]{x^2}+x^4\right)\mathrm{d}x \]

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

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

$ -\frac{4}{5} $

$- \frac{1}{5} $

2010000001

Level:

Vypočítejte určitý integrál. \[ \int\limits_1^2\left(5^x \cdot\ln5 -x^5-4x\right)\mathrm{d}x \]

$ \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)=ax^4+bx $, find real numbers $ a $ and $ b $, such that $ \int\limits_0^1f(x)\,\mathrm{d}x=27 $ and $ \int\limits_{-1}^0f(x)\,\mathrm{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(\pi;2\pi) $ makes the equality $ \int\limits_{\pi}^{a+\pi} \sin⁡2x\,\mathrm{d}x=1 $ true?

$ a=\frac32\pi $

$ a=\frac34\pi $

$ a=\frac12\pi $

$ a=\frac23\pi $

1003124307

Level:

Which of the positive values of a real number $a$ makes the equality $\int\limits_a^7 \frac{6x-5}{3x^2-5x}\,\mathrm{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\limits_1^a \frac3{3x+5}\,\mathrm{d}x=\ln\frac74 $ true?

$ a = 3 $

$ a = 2 $

$ a = 4 $

$ a = 5 $

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

Definite integral

2000000901

2010000003

2010000002

2010000001

Equations with Definite Integral