TS EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \frac{d x}{4+5 \sin x}\)
- A \(\frac{1}{2} \log 3\)
- B \(\frac{1}{3} \log 2\)
- C \(2 \log 3\)
- D \(\frac{1}{2} \log \frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3} \log 2\)
Step-by-step Solution
Detailed explanation
We have, \(\int_0^{\pi / 2} \frac{d x}{4+5 \sin x}\) \(=\int_0^{\pi / 2} \frac{d x}{4+5\left(\frac{2 \tan \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}\right)}\) \(=\int_0^{\pi / 2} \frac{\left(1+\tan ^2 \frac{x}{2}\right)}{4+4 \tan ^2 \frac{x}{2}+10 \tan \frac{x}{2}} d x\)…
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
- Consider the fourteen lines in the plane given by \(y=x+r, \quad y=-x+r, \quad\) where \(r \in\{0,1,2,3,4,5,6\}\). The number of squares formed by these lines, whose sides are of length \(\sqrt{2}\), is :TS EAMCET 2003 Medium
-
The correct match is
TS EAMCET 2019 Hard - Let \(A\) and \(B\) be events in a sample space \(S\) such that \(P(A)=0.5, \quad P(B)=0.4\) and \(P(A \cup B)=0.6\). Observe the following lists.
The correct match of List I from List II is (i) (ii) (iii) (iv)TS EAMCET 2011 Medium - The nearest approximate value of \(\sqrt{2023}\) isTS EAMCET 2023 Easy
- The Rolle's theorem is not applicable to on becauseTS EAMCET 2021 Easy
- If the slopes of the lines represented by the equation \(6 x^2+2 h x y+4 y^2=0\) are in the ratio \(2: 3\), then the value of h such that both the lines make acute angles with the positive X -axis measured in positive direction isTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- A straight rod of length \(L\) is made of a material having mass per unit length \(m(x)=\lambda|x|\), where \(x\) is measured from the centre of rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod will be \(L=1 \mathrm{~m}\) and \(\lambda=16 \mathrm{~kg} / \mathrm{m}^2\).TS EAMCET 2020 Medium
- Two resistances of \(400 \Omega\) and \(800 \Omega\) are connected in series with \(6 \mathrm{~V}\) battery of negligible internal resistance. A voltmeter of resistance \(10000 \Omega\) is used to measure the potential difference across \(400 \Omega\). The error in the measurement of potential difference in volts approximately is :TS EAMCET 2003 Medium
- Angles made with the \(X\)-axis by the two lines passing through the point \(P(1,2)\) and cutting the line \(x+y=4\) at a distance \(\frac{\sqrt{6}}{3}\) units from the point \(P\) areTS EAMCET 2020 Easy
- A ball of mass moving with a speed of hits another ball of mass moving in the same direction with a speed of . If the kinetic energy of center of mass is , then the magnitude of isTS EAMCET 2020 Easy
- The moment of intertia of a solid cylinder of mass \(M\), length \(2 R\) and radius \(R\) about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is \(I_1\) and about an axis passing through one end of the cylinder and perpendicular to the axis of the cylinder is \(I_2\), thenTS EAMCET 2015 Medium
- Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as \(r=r_0 e^{-\alpha x}\), where \(\alpha=\frac{1}{3} \mathrm{~m}^{-1}\) and \(x\) is the distance from the pipeline inlet. If \(R_1\) is the Reynold's number for a certain pipeline cross-section at a distance \(x_1\) metre from the inlet and \(R_2\) is for distance \(\left(x_1+3\right)\) metre, then the ratio \(\frac{R_1}{R_2}\) isTS EAMCET 2020 Medium