Question:
If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $
If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $
Updated On: Jun 23, 2024
- $-1$
- $\frac{1}{2} $
- $ - \frac{1}{2} $
- $1$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Answer (d) $1$
Was this answer helpful?
0
1
Top Questions on Integrals of Some Particular Functions
- The integral \(16 \int\limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\) is equal to
- JEE Main - 2023
- Mathematics
- Integrals of Some Particular Functions
- If \(\int \frac{dx}{(x+1)(x-2)(x-3)}=\frac{1}{k}log_e\left \{ \frac{|x-3|^3|x+1|}{(x-2)^4}\right \}+c\), then the value of k is
- WBJEE - 2023
- Mathematics
- Integrals of Some Particular Functions
- Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$ If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to
- JEE Main - 2023
- Mathematics
- Integrals of Some Particular Functions
- If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______
- JEE Main - 2023
- Mathematics
- Integrals of Some Particular Functions
- If $\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{ k \pi}{16}$, then $k$ is equal to
- JEE Main - 2023
- Mathematics
- Integrals of Some Particular Functions
View More Questions
Questions Asked in MHT CET exam
- Total genetic content of an organism is called
- MHT CET - 2024
- Non-Mendelian Genetics
- Two monkeys off mass 10 kg and 8 kg are moving along a vertical light rope the former climbing up with an acceleration of 2 m/second square while the latter coming down with a uniform velocity of 2 m/sec square find the tension in the rope at the fixed support
- MHT CET - 2024
- tension
- Which disease is primarily spread by female Anopheles mosquitoes?
- MHT CET - 2024
- HIV and AIDS
- How many ATP molecules are needed as an initial investment in the glycolytic cycle (normal glycolysis)?
- MHT CET - 2024
- Glycolysis
- If \(A=\begin{bmatrix} 2a & -3b\\ 3 & 2\end{bmatrix}\) and \(\text{adj}A = AA^T\), then 2a+3b is?
- MHT CET - 2023
- Matrices
View More Questions
Concepts Used:
Integrals of Some Particular Functions
There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
Integrals of Some Particular Functions:
- ∫1/(x2 – a2) dx = (1/2a) log|(x – a)/(x + a)| + C
- ∫1/(a2 – x2) dx = (1/2a) log|(a + x)/(a – x)| + C
- ∫1/(x2 + a2) dx = (1/a) tan-1(x/a) + C
- ∫1/√(x2 – a2) dx = log|x + √(x2 – a2)| + C
- ∫1/√(a2 – x2) dx = sin-1(x/a) + C
- ∫1/√(x2 + a2) dx = log|x + √(x2 + a2)| + C
These are tabulated below along with the meaning of each part.
