AP EAMCET · Maths · Indefinite Integration
\(\int \frac{5 \tan x}{(\tan x)-2} d x=\alpha x+\beta \log |\sin x-2 \cos x|\) \(+\gamma\), then \(\alpha-\beta=\)
- A –1
- B 2
- C 0
- D 1
Answer & Solution
Correct Answer
(A) –1
Step-by-step Solution
Detailed explanation
\(\int \frac{5 \tan x}{\tan x-2} d x=\int \frac{5 \sin x}{\sin x-2 \cos x} d x\) Put, \(5 \sin x=\alpha(\sin x-2 \cos x)+\) \[ \begin{array}{r} \beta \frac{d}{d x}(\sin x-2 \cos x) \\ 5 \sin x=\alpha(\sin x-2 \cos x)+\beta(\cos x+2 \sin x) \end{array} \] On comparison of…
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 \(f(x)=\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}\). If \(\lim _{x \rightarrow m} f(x)=5 / 2\), then set of all possible finite values of 1 and \(m\) isAP EAMCET 2023 Easy
- A plane passes through the point . If the direction ratios of its normal are equal to the intercepts made by the plane with the coordinate axes, then the equation of that plane isAP EAMCET 2018 Medium
- If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is \(90^{\circ}\), then it eccentricity isAP EAMCET 2022 Medium
- If \(4 x^2-5 x y+y^2=0\) represents a pair of lines with slopes \(m_1\) and \(m_2\), then the value of \(\left|m_1-m_2\right|\) equalsAP EAMCET 2021 Medium
- If \(y=4 \cos ^3(t)\) and \(x=4 \sin ^3(t)\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2021 Medium
- The point dividing the join of \((3,-2,1)\) and \((-2,3,11)\) in the ratio \(2: 3\) isAP EAMCET 2010 Easy
More PYQs from AP EAMCET
- \(\int \frac{d x}{\sin (x-a) \cos (x-b)}=\)AP EAMCET 2023 Medium
- \(C_1\) is the circle with centre at \(O(0,0)\) and radius \(4, C_2\) is a variable circle with centre at \((\alpha, \beta)\) and radius 5 . If the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) has slope \(\frac{3}{4}\) and of maximum length, then one of the possible values of \(\alpha+\beta\) isAP EAMCET 2024 Medium
- An electronic transition in hydrogen atom results in the formation of \(\mathrm{H}_\alpha\) line of hydrogen in Lyman series, the energies associated with the electron in each of the orbits involved in the transition (in kcal \(\mathrm{mol}^{-1}\) ) areAP EAMCET 2008 Medium
- Find the apparent weight of a body of mass \(1.0 \mathrm{~kg}\) falling with an acceleration of \(10 \mathrm{~ms}^{-2}\). \(\left(g \approx 10 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2020 Easy
- If all the seven letters of the word LEADING are permuted in all possible ways and the words thus formed are arranged as in the dictionary order, then the word in place isAP EAMCET 2018 Easy
- The length of the chord intercepted by the circle \(x^2+y^2-4 x+6 y-12=0\) on the line \(4 x+3 y+1=0\) isAP EAMCET 2017 Easy