AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{5 \tan \mathrm{x}}{\tan \mathrm{x}-2} \mathrm{dx}=\mathrm{ax}+\mathrm{b} \log |\sin \mathrm{x}-2 \cos \mathrm{x}|+\mathrm{c}\), then \(\mathrm{a}+\mathrm{b}=\)
- A \(2\)
- B \(3\)
- C \(4\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\( \int \frac{5 \tan x}{\tan x - 2} dx = \int \frac{5 \sin x}{\sin x - 2 \cos x} dx \) Let \( 5 \sin x = A(\sin x - 2 \cos x) + B(\cos x + 2 \sin x) \) \( A+2B=5 \) \( -2A+B=0 \Rightarrow B=2A \) \( A+2(2A)=5 \Rightarrow 5A=5 \Rightarrow A=1 \) \( B=2(1)=2 \)…
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
- If the range of the function \(f(x)=-3 x-3\) is \(\{3,-6,-9,-18\}\), then which one of the following is not in the domain of f ?AP EAMCET 2025 Easy
- If the equation of the pair of straight lines intersecting at \((a, b)\) and perpendicular to the pair of lines \(3 x^2-4 x y+5 y^2=0\) is \(l x^2+2 h x y+m y^2-32 x-26 y+c=0\), then \(\frac{a+b+c}{l+h+m}=\)AP EAMCET 2025 Hard
- The solution set of the inequation \(\sqrt{x^2+6 x+5}>(8-x)\) isAP EAMCET 2018 Easy
- The distance of a point \((2,3,-5)\) from the plane \(\vec{r} \cdot(4 \hat{i}-3 \hat{j}+2 \hat{k})=4\) isAP EAMCET 2024 Easy
- The coefficient of \(x^2\) in the expansion of \((1+x)^2(8-x)^{-\frac{1}{3}}\) isAP EAMCET 2017 Medium
- If the tangent at the point \(\left(4 \cos 2 \theta, \frac{16}{\sqrt{11}} \sin 2 \theta\right)\) on the ellipse \(16 x^2+11 y^2=256\) touches the circle \(x^2+y^2-2 x=15\), then \(\theta=\)AP EAMCET 2018 Easy
More PYQs from AP EAMCET
- From consonants and vowels, how many words can be formed using consonants and vowels?AP EAMCET 2020 Medium
- The maximum number of sub-levels, orbitals and electrons in \(N\) shell of an atom are respectivelyAP EAMCET 2007 Easy
- A slab B rests on a frictionless floor as shown in the figure. A block A rests on top of the slab- B. The coefficients of static and kinetic friction between the block A and the slab B are and respectively. When block-A is acted upon by a horizontal force of , as shown, find the resulting acceleration of the slab- B.
AP EAMCET 2021 Hard - If \(z\) is complex number such that \(\left|z-\frac{4}{z}\right|=2\), then the greatest value of \(|z|\) isAP EAMCET 2012 Medium
- The height of ceiling in an auditorium is 30 m. A ball is thrown with a speed of \(30 \mathrm{~m} \mathrm{~s}^{-1}\) from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then the length of auditorium is
[Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) ]AP EAMCET 2025 Medium - \(3.011 \times 10^{22}\) atoms of an element weighs \(1.15 \mathrm{~g}\). The atomic mass of the element isAP EAMCET 2015 Medium