Question:
if $∫_{-1}^1 \frac{cos \, \alpha x}{1+3^x} dx = \frac2{\pi} $ then $\alpha$ is
if $∫_{-1}^1 \frac{cos \, \alpha x}{1+3^x} dx = \frac2{\pi} $ then $\alpha$ is
Updated On: Apr 14, 2024
- π/6
- π/2
- π/3
- π
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The Correct answer is option(B) : π/2
Was this answer helpful?
0
1
Top Questions on Definite Integral
- Evaluate the integral $\int_0^1 \frac{a - bx^2}{(a + bx^2)^2} , dx$:
- 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
- \(Evaluate \int_0^{\pi/2} \frac{1 - \cot x}{\csc x + \cos x} \, dx:\)
- 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
- Find the value of \[ \sin 70^\circ \left( \cot 10^\circ \cot 70^\circ - 1 \right). \]
- JEE Main - 2025
- Miscellaneous
The value of current \( I \) in the electrical circuit as given below, when the potential at \( A \) is equal to the potential at \( B \), will be _____ A.
- JEE Main - 2025
- Digital Circuits
Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = \frac{4}{3} \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \left( \frac{n_2}{2n_1} \right) \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is …….. cm.
- JEE Main - 2025
- Units and measurement
- Suppose that the number of terms in an A.P. is \( 2k, k \in \mathbb{N} \). If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then \( k \) is equal to:
- JEE Main - 2025
- Arithmetic Progression
- Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:
- JEE Main - 2025
- System of Particles & Rotational Motion
View More Questions