enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(f\left( {\frac{{3x - 4}}{{3x + 4}}} \right) = x + 2,\,x \ne -\frac{4}{3}\) , and \(\int {f\left( x \right)dx = A\,\log \left| {1 - x} \right| + Bx + C} \) , then the ordered pair \((A,B) \) is equal to : (where \(C\) is a constant of integration)
- A \(\left( {\frac{8}{3},\frac{2}{3}} \right)\)
- B \(\left( { - \frac{8}{3},\frac{2}{3}} \right)\)
- C \(\left( { - \frac{8}{3}, - \frac{2}{3}} \right)\)
- D \(\left( {\frac{8}{3}, - \frac{2}{3}} \right)\)
Answer & Solution
Correct Answer
(B) \(\left( { - \frac{8}{3},\frac{2}{3}} \right)\)
Step-by-step Solution
Detailed explanation
\(f\left(\frac{3 x-4}{3 x+4}\right)=x+2, x \neq-\frac{4}{3}\) Consider \(\frac{3 x-4}{3 x+4}=t\) \(3 x-4=3 t x+4 t\) \(x=\frac{4 t+4}{3-3 t}+2\) \(f(t)=\frac{10-2 t}{3-3 t}\) \(f(x) = \frac{{2x - 10}}{{3x - 3}}\) \(\int f (x)dx = \int {\frac{{2x - 10}}{{3x - 3}}} dx\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(f : R \rightarrow R\) be a differentiable function such that \(f \left(\frac{\pi}{4}\right)=\sqrt{2}, f \left(\frac{\pi}{2}\right)=0\) and \(f ^{\prime}\left(\frac{\pi}{2}\right)=1\) and let \(g(x)=\int\limits_{x}^{\pi / 4}\left(f^{\prime}(t) \sec t+\tan t \operatorname{sectf}(t)\right) d t\) for \(x \in\left[\frac{\pi}{4}, \frac{\pi}{2}\right)\). Then \(\lim\limits _{ x \rightarrow\left(\frac{\pi}{2}\right)^{-}} g ( x )\) is equal toJEE Mains 2022 Hard
- Let \(A=\left[a_{i j}\right]\) be a square matrix of order 2 with entries either 0 or 1 . Let \(E\) be the event that \(A\) is an invertible matrix. Then the probability \(\mathrm{P}(\mathrm{E})\) is :JEE Mains 2025 Easy
- Let \(n \geq 5\) be an integer. If \(9^{n}-8 n-1=64 \alpha\) and \(6^{ n }-5 n -1=25 \beta\), then \(\alpha-\beta\) is equal toJEE Mains 2022 Medium
- If the four points, whose position vectors are \(3 \hat{ i }-4 \hat{ j }+2 \hat{ k }, \hat{ i }+2 \hat{ j }-\hat{ k },-2 \hat{ i }-\hat{ j }+3 \hat{ k } \quad\) and \(5 \hat{ i }-2 \alpha \hat{ j }+4 \hat{ k }\) are coplanar, then \(\alpha\) is equal toJEE Mains 2023 Medium
- Let \(\vec \alpha =(\lambda -2) \vec a + \vec b\) and \(\vec \beta = (4\lambda -2)\vec a + 3\vec b\) be two given vectors where \(\vec a\) and \(\vec b\) are non collinear. The value of \(\lambda \) for which vectors and \(\vec \alpha \) and \(\vec \beta \) are collinear, isJEE Mains 2019 Medium
- Let \(f:R \to R\) be a continuously differentiable function such that \(f\left( 2 \right) = 6\) and \(f'\left( 2 \right) = \frac{1}{{48}}\). If \(\int_6^{f\left( x \right)} {4{t^3}} \,dt = \left( {x - 2} \right)\,g\left( x \right)\), then \(\mathop {\lim }\limits_{x \to 2} \,g\left( x \right)\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(A\) be a \(3 \times 3\) matrix with \(\operatorname{det}( A )=4\). Let \(R _{ i }\) denote the \(i ^{\text {th }}\) row of \(A\). If a matrix \(B\) is obtained by performing the operation \(R _{2} \rightarrow 2 R _{2}+5 R _{3}\) on \(2 A ,\) then \(\operatorname{det}( B )\) is equal to ...... .JEE Mains 2021 Medium
- The total number of three-digit numbers, divisible by \(3\) , which can be formed using the digits \(1,3,5,8\) , if repetition of digits is allowed, is:JEE Mains 2023 Medium
- Let \(y=y(x)\) be the solution of the differential equation \(\left(1+y^2\right) e^{\tan x} d x+\cos ^2 x\left(1+e^{2 \tan x}\right) d y=0\), \(y(0)=1\). Then \(y\left(\frac{\pi}{4}\right)\) is equal to :JEE Mains 2024 Medium
- If \(y = y ( x )\) is the solution of the differential equation \(\left(1+ e ^{2 x }\right) \frac{ dy }{ dx }+2\left(1+ y ^{2}\right) e ^{ x }=0\) and \(y (0)=0\), then \(6\left( y ^{\prime}(0)+\left( y \left(\log _{ e } \sqrt{3}\right)\right)^{2}\right)\) is equal toJEE Mains 2022 Hard
- The term independent of \(x\) in the expansion of \(\left[\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right]^{10}, x \neq 1,\) is equal to ....... .JEE Mains 2021 Hard
- Consider the matrix \(f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]\) Given below are two statements: Statement I: \(f(-x)\) is the inverse of the matrix \(f(x)\). Statement II: \(f(x) f(y)=f(x+y)\). In the light of the above statements, choose the correct answer from the options given belowJEE Mains 2024 Hard