AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{a \cos x+3 \sin x}{5 \cos x+2 \sin x} d x=\frac{26}{29} x-\frac{k}{29} \log |5 \cos x+2 \sin x|+c\), then \(|a+k|=\)
- A \(3\)
- B \(11\)
- C \(12\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\(a \cos x+3 \sin x = A(5 \cos x+2 \sin x) + B(-5 \sin x+2 \cos x)\) \(A = \frac{26}{29}, B = -\frac{k}{29}\) \(a = 5A+2B \Rightarrow a = 5(\frac{26}{29}) + 2(-\frac{k}{29})\) \(3 = 2A-5B \Rightarrow 3 = 2(\frac{26}{29}) - 5(-\frac{k}{29})\) \(3 = \frac{52}{29} + \frac{5k}{29}\)…
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
- For a positive real number \(\lambda\), if the vector \(\hat{\mathrm{a}}=\lambda \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}\) satisfies the equation \([\hat{\mathrm{i}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{i}})+\hat{\mathrm{j}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{j}})+\hat{\mathrm{k}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{k}})]^2=440\), then \(\lambda=\)AP EAMCET 2023 Medium
- If is a continuous real-valued function, then the range of the function is _______AP EAMCET 2020 Easy
- \(\int_0^1 \frac{x}{(1-x)^{3 / 4}} d x=\)AP EAMCET 2024 Medium
- \(\sin ^{-1} \frac{4}{5}+2 \tan ^{-1} \frac{1}{3}\) is equal toAP EAMCET 2005 Medium
- The set \(\left\{x \in \mathbb{R}: 16\left(2^X\right)>16^{\frac{-1}{x}}\right\}=\)AP EAMCET 2023 Easy
- The transformed equation \(3 x^2+3 y^2+2 x y=2\), when the coordinate axes are rotated through an angle \(45^{\circ}\) isAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- The value of \(\tan 40^{\circ}+\tan 11^{\circ}+\tan 20^{\circ}-\tan 56^{\circ}+\tan 56^{\circ} \tan 11^{\circ}+\sqrt{3} \tan 40^{\circ} \tan 20^{\circ}\) isAP EAMCET 2018 Medium
- \(\mathrm{A} \rightarrow \mathrm{P}\) is a zero order reaction. At 298 K the rate constant of the reaction is \(1 \times 10^{-3} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\). Initial concentration of ' \(A\) ' is \(0.1 \mathrm{~mol} \mathrm{~L}^{-1}\). What is the concentration of ' \(A\) ' after 10 sec ?AP EAMCET 2019 Easy
- The pressure and density of a given mass of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\) change adiabatically from \((P, d)\) to \(\left(P^{\prime}, d^{\prime}\right)\). If \(\frac{d^{\prime}}{d}=32\), then \(\frac{P^{\prime}}{P}\) is ( \(\gamma=\) ratio of specific heats \()\)AP EAMCET 2004 Medium
- If \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is a real number and \(0 < \theta < 2 \pi\), then \(\theta\) is equal toAP EAMCET 2002 Easy
- The equation of the pair of lines through the point \((2,1)\) and perpendicular to the pair of lines \(4 x y+2 x+6 y+3=0\) isAP EAMCET 2017 Medium
- In a \(\triangle A B C\), if \(r_1=36, r_2=18\) and \(r_3=12\), then \(s=\)AP EAMCET 2022 Medium