AP EAMCET · Maths · Definite Integration
\(\int_0^\pi \frac{x \sin x}{\sin ^2 x+2 \cos ^2 x} d x=\)
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi^2}{2}\)
- C \(\frac{\pi^2}{4}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi^2}{4}\)
Step-by-step Solution
Detailed explanation
\(I = \int_0^\pi \frac{x \sin x}{\sin ^2 x+2 \cos ^2 x} d x\) \(I = \int_0^\pi \frac{(\pi-x) \sin (\pi-x)}{\sin ^2 (\pi-x)+2 \cos ^2 (\pi-x)} d x = \int_0^\pi \frac{(\pi-x) \sin x}{\sin ^2 x+2 \cos ^2 x} d x\)…
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
- If \(2 \hat{i}+\hat{j}-\hat{k}, \hat{i}-3 \hat{j}+5 \hat{k}\) and \(-3 \hat{i}+4 \hat{j}+4 \hat{k}\) are the position vectors of three points A, B and C respectively, thenAP EAMCET 2023 Easy
- If \(a \neq 1, b \neq-1, c \neq-1\) and the system of equations, \(x=a(y+z), y=b(z+x), z=c(x+y)\) has a non-trivial solution, then.AP EAMCET 2018 Medium
- If \(\frac{\mathrm{k}}{\mathrm{kx}+3}+\frac{3}{3 \mathrm{x}-\mathrm{k}}=\frac{12 \mathrm{x}+5}{(\mathrm{kx}+3)(3 \mathrm{x}-\mathrm{k})} \forall \mathrm{x} \in \mathrm{R}\)
\(-\left\{\frac{\{3\}}{\mathrm{k}}, \frac{\mathrm{k}}{3}\right\}\), then both the roots of the equation \(\mathrm{kx}^2-7 \mathrm{x}+3=0\) areAP EAMCET 2023 Medium - The smallest integer \(n\) such that \(\frac{1}{\sin 45^{\circ} \sin 46^{\circ}}+\frac{1}{\sin 47^{\circ} \sin 48^{\circ}}+\ldots\) \(+\frac{1}{\sin 133^{\circ} \sin 134^{\circ}}=\frac{1}{\sin \left(n^0\right)}\) isAP EAMCET 2022 Easy
- Let \(\theta \in R\) such that \(3 \sinh (2 \theta)=13-3 e^{2 \theta}\), then \(\theta=\)AP EAMCET 2022 Medium
- If \(\int \frac{d x}{e^x+4 e^{-x}} d x=f(x)+c\), then \(f(x)\) isAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- amperes of current is passed for seconds through an aqueous solution using platinum electrodes. The mass of copper consumed from the solution and volume of gas liberated at STP are respectively (molar mass of )AP EAMCET 2022 Medium
- Match the following
\(\begin{array}{llll}
& \text {List - I} & & \text {List - II} \\
\text {a)} & \text {See Saw Shape} & \text {i)} & \mathrm{XeF}_4 \\
\text {b)} & \text {Square Pyramidal} & \text {ii)} & \mathrm{CF}_3 \\
\text {c)} & \text {T-Shape} & \text {iii)} & \mathrm{PbCl}_2 \\
\text {d)} & \text{Bent Shape} & \text {iv)} & \mathrm{SF}_4 \\
& & \text {v)} & \mathrm{BrF}_5
\end{array}\)
The correct answer isAP EAMCET 2017 Medium - The difference between the radii of and orbits of hydrogen atom is equal to the radius of orbit of hydrogen. The angular momentum of the electron in the orbit is( is Planck's constant)AP EAMCET 2018 Medium
- Order of acidity of benzoic acid (I), 4-methoxybenzoic acid (II), acetic acid (III) and 4-nitrobenzoic acid (IV) isAP EAMCET 2018 Medium
- A lift raises 50 passengers each having average weight \(600 \mathrm{~N}\) to a height of \(100 \mathrm{~m}\) at a constant speed in time \(t\). If the average power of \(15 \mathrm{~kW}\) is required by the lift, then the value of \(t\) in seconds isAP EAMCET 2022 Easy
- The incorrect statement about amylose isAP EAMCET 2025 Medium