AP EAMCET · Maths · Definite Integration
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta\) is equal to
- A \(0\)
- B \(1\)
- C \(2\)
- D \(-1\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta\) Let \(\quad f(\theta)=\log \left(\frac{2-\sin \theta}{2+\sin \theta}\right)\)…
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
- The angle between the curves \(\mathrm{y}^2=\mathrm{x}\) and \(\mathrm{x}^2=\mathrm{y}\) at the point \((1,1)\) isAP EAMCET 2025 Medium
- In triangle ABC, if \(\mathrm{a}=13, \mathrm{~b}=8, \mathrm{c}=7\), then \(\cos (\mathrm{B}+\mathrm{C})=\)AP EAMCET 2025 Medium
- If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity isAP EAMCET 2022 Easy
- \(\begin{aligned} & \frac{1}{x(x+1)(x+2) \ldots(x+n)}=\frac{A_0}{x}+\frac{A_1}{x+1} \\ & +\ldots \frac{A_n}{x+n}, 0 \leq i \leq r \Rightarrow A_r \text { is equal to }\end{aligned}\)AP EAMCET 2012 Hard
- \(\mathrm{P}\) is a point of intersection of the circles \(\mathrm{S} \equiv \mathrm{x}^2+\mathrm{y}^2-6 \mathrm{x}\) \(+2 k y+1=0\) and \(S^1 \equiv x^2+y^2+2 k x-6 y-7=0\). If the tangent at \(P\) to \(S=0\) pass through the centre of \(S^1=0\) and the tangent at \(\mathrm{P}\) to \(\mathrm{S}^1=0\) pass through the centre of \(\mathrm{S}=0\), then the radius of \(\mathrm{S}^1=0\) isAP EAMCET 2023 Medium
- Among the following functions defined on \(\mathbb{R}\) into \(\mathbb{R}\), the constant function isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- \(\int e^{x / 2}\left(\frac{2+\sin x}{1+\cos x}\right) d x=\)AP EAMCET 2020 Hard
- If \(k \in N\), then \(3^{3 k}-26^k-1\) is divisible byAP EAMCET 2020 Medium
- If the pair of straight lines \(x y-x-y+1=0\) and the line \(a x+2 y-3 a=0\) are concurrent, then \(a\) is equal toAP EAMCET 2002 Medium
- Which one of the following represents the correct order of electronegativity?AP EAMCET 2002 Easy
- Let \(A B C\) be an equilateral triangle of side \(a . M\) and \(N\) are two points on the sides \(A B\) and \(A C\) respectively such that \(\overrightarrow{\mathrm{AN}}=\mathrm{K} \overrightarrow{\mathrm{AC}}\) and \(\overrightarrow{\mathrm{AB}}=3 \overrightarrow{\mathrm{AM}}\). If the vectors \(\overrightarrow{\mathrm{BN}}\) and \(\overrightarrow{\mathrm{CM}}\) are perpendicular, then \(\mathrm{K}=\)AP EAMCET 2024 Easy
- If \(\frac{x-4}{x^2-5 x+6}\) can be expanded in the ascending powers of \(x\), then the coefficient of \(x^3\) isAP EAMCET 2004 Medium