Question:
\( \int_0^\infty \left( \sin x + \left| \sin x \right| \right) dx \) is equal to?
\( \int_0^\infty \left( \sin x + \left| \sin x \right| \right) dx \) is equal to?
Show Hint
For integrals involving periodic functions like \( \sin x \), break the integral into regions where the function has a consistent sign.
Updated On: Jan 12, 2026
- 0
- 4
- 8
- 1
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The integral involves the periodic nature of the sine function, and by splitting the integral at points where the sine function changes its sign, we can evaluate it to get 8.
Was this answer helpful?
0
0
Top Questions on Some Properties of Definite Integrals
- Find the area bounded by \( y = \max \{ \sin x, \cos x \} \) when \( x \in \left[ 0, \frac{3\pi}{2} \right] \) with the x-axis:
- JEE Main - 2026
- Mathematics
- Some Properties of Definite Integrals
- The value of \[ \int_{\frac{\pi}{24}}^{\frac{5\pi}{24}} \frac{1}{1 + \sqrt{\tan 2x}} \, dx \] is:
- JEE Main - 2026
- Mathematics
- Some Properties of Definite Integrals
Match List-I with List-II
List-I (Definite integral) List-II (Value) (A) \( \int_{0}^{1} \frac{2x}{1+x^2}\, dx \) (I) 2 (B) \( \int_{-1}^{1} \sin^3x \cos^4x\, dx \) (II) \(\log_e\!\left(\tfrac{3}{2}\right)\) (C) \( \int_{0}^{\pi} \sin x\, dx \) (III) \(\log_e 2\) (D) \( \int_{2}^{3} \frac{2}{x^2 - 1}\, dx \) (IV) 0
Choose the correct answer from the options given below:- CUET (UG) - 2025
- Mathematics
- Some Properties of Definite Integrals
- $\int_{\pi/6}^{\pi/3} \frac{\tan x}{\tan x + \cot x} dx$ is equal to
- CUET (UG) - 2025
- Mathematics
- Some Properties of Definite Integrals
- $\int_{1}^{4} |x - 2| dx$ is equal to
- CUET (UG) - 2025
- Mathematics
- Some Properties of Definite Integrals
View More Questions
Questions Asked in VITEEE exam
- Find the value of \( x \) in the following equation: \[ \frac{2}{x} + \frac{3}{x + 1} = 1 \]
- VITEEE - 2025
- Algebra
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Data Interpretation
- TUV : VYB :: PRA : ?
- VITEEE - 2025
- Odd one Out
- What is the pH of a solution with a \( \text{H}^+ \) concentration of \( 1 \times 10^{-3} \) mol/L?
- VITEEE - 2025
- Solubility Equilibria Of Sparingly Soluble Salts
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Odd one Out
View More Questions