Question:
$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?
$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?
Updated On: Apr 6, 2024
- $π^2$
- $2π$
- $\frac{3π}2$
- $\frac{π^2}2$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The Correct answer is option is (A) : $π^2$
Was this answer helpful?
0
0
Top Questions on Definite Integral
- \(Evaluate \int_0^{\pi/2} \frac{1 - \cot x}{\csc x + \cos x} \, dx:\)
- CUET (UG) - 2024
- Mathematics
- Definite Integral
- The value of the integral \( \int_{\ln 2}^{\ln 3} \frac{e^{2x} - 1}{e^{2x} + 1} \, dx \) is:
- CUET (UG) - 2024
- Mathematics
- Definite Integral
- Evaluate the integral $\int_0^1 \frac{a - bx^2}{(a + bx^2)^2} , dx$:
- CUET (UG) - 2024
- Mathematics
- Definite Integral
- Match List I with List IIChoose the correct answer from the options given below :
List I List II A. \(\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\frac{7}{2}}x}{\sin^{\frac{7}{2}}+\cos^{\frac{7}{2}}}dx\) I. \(\frac{\pi}{4}-\frac{1}{2}\) B. \(\int\limits_0^{\pi}\frac{x\sin x}{1+\cos^2x}dx\) II. 0 C. \(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}x\cos x\ dx\) III. \(\frac{\pi}{4}\) D. \(\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^2x\ dx\) IV. \(\frac{\pi^2}{4}\) - CUET (UG) - 2023
- Mathematics
- Definite Integral
- The integral \(\int_0^1x(1-x)^n dx\) is equal to :
- CUET (UG) - 2023
- Mathematics
- Definite Integral
View More Questions
Questions Asked in JEE Main exam
- Let \( \alpha_1 \) and \( \beta_1 \) be the distinct roots of \( 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) \). If \( m \) and \( M \) are the minimum and the maximum values of \( \alpha_1 + \beta_1 \), then \( 16(M + m) \) equals:
- JEE Main - 2025
- Binomial Expansion
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
- The greatest value of \( n \), where \( n \in \mathbb{N} \), such that \( 3^n \) divides \( 50! \) is:
- JEE Main - 2025
- Number Systems
- Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
- JEE Main - 2025
- Trigonometry
- In 3, 3-dimethylhex-1-en-4-yne, the number of sp, sp² and sp³ carbon atoms, respectively are:
- JEE Main - 2025
- Organic Chemistry
View More Questions