The value of the integral
\[
\int_0^0 9 [x - 2\lfloor x \rfloor] \, dx
\]
where \( [.] \) denotes the greatest integer function, is
Show Hint
- 0.9
- 0
- 1.8
- -0.9
The Correct Option is B
Solution and Explanation
The result is \( 0 \).
Top Questions on Integration
- Solve \( \int_{-1}^{1} \frac{1+2x}{e^{-x} + e^x} \, dx \).
- JEE Main - 2025
- Mathematics
- Integration
For the beam and loading shown in the figure, the second derivative of the deflection curve of the beam at the mid-point of AC is given by \( \frac{\alpha M_0}{8EI} \). The value of \( \alpha \) is ........ (rounded off to the nearest integer).
- GATE CE - 2025
- Mathematics
- Integration
If the function \[ f(x) = \begin{cases} \frac{2}{x} \left( \sin(k_1 + 1)x + \sin(k_2 -1)x \right), & x<0 \\ 4, & x = 0 \\ \frac{2}{x} \log_e \left( \frac{2 + k_1 x}{2 + k_2 x} \right), & x>0 \end{cases} \] is continuous at \( x = 0 \), then \( k_1^2 + k_2^2 \) is equal to:
- JEE Main - 2025
- Mathematics
- Integration
The integral is given by:
\[ 80 \int_{0}^{\frac{\pi}{4}} \frac{\sin\theta + \cos\theta}{9 + 16 \sin 2\theta} d\theta \]
is equals to?
- JEE Main - 2025
- Mathematics
- Integration
- If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then \( (a + \beta)^2 \) equals:
- JEE Main - 2025
- Mathematics
- Integration
Questions Asked in IPU CET exam
Which of the following is an octal number equal to decimal number \((896)_{10}\)?
- IPU CET - 2023
- Binary Operations
The additional 8% human genome sequenced account for ........ million new letters added to the existing sequenced DNA.
- IPU CET - 2023
- Genomics, proteomics, metabolomics
- Which of the following statements are true or false?
I. Endemic when it spreads across the globe is called a pandemic.
II. Epidemic is a disease that is permanently present in a region or population
Which of the following options is correct?- IPU CET - 2023
- Epidemiology
- Which one among the following is not a characteristic of 'big data'?
- IPU CET - 2023
- Big Data
- Blockchain Technology has the following hall mark features/s:
- IPU CET - 2023
- Blockchain Technology