AP EAMCET · Maths · Definite Integration
\(\int_0^{\pi 6} \cos ^4 3 \theta \cdot \sin ^2 6 \theta d \theta\) equals to
- A \(\frac{\pi}{96}\)
- B \(\frac{5}{192}\)
- C \(\frac{5 \pi}{256}\)
- D \(\frac{5 \pi}{192}\)
Answer & Solution
Correct Answer
(D) \(\frac{5 \pi}{192}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^{\pi / 6} \cos ^4 3 \theta \sin ^2 6 \theta d \theta\) Put \(3 \theta=t \Rightarrow d \theta=\frac{d t}{3}\)…
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 equations of sides \(\mathbf{A B}, \mathbf{B C}\) and \(\mathbf{C A}\) of a \(\triangle A B C\) are \(2 x+y=0, x+p y=q\) and \(x-y=3\) respectively. If \(P(2,3)\) is its orthocenter, then the value of \(p+q\) equalsAP EAMCET 2021 Hard
- If \(\int \log \left(a^2+x^2\right) d x=h(x)+C\), then \(\mathrm{h}(x)\) is equal toAP EAMCET 2016 Medium
- Assertion (A): \(\int_{\frac{\pi}{2}}^{\frac{3 \pi}{2}}[2 \sin x] d x=0\), where [.] denotes the greatest integer function
Reason (R) : \(2 \sin x\) is a decreasing function in \(\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]\)AP EAMCET 2023 Easy - If the period of the function \(f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}\) is \(\alpha\), then
\((\alpha)\) \(f\left(\frac{\boldsymbol{\alpha}}{8}\right)=\)AP EAMCET 2024 Medium - In a triangle, if the ex-radii \(r_1, r_2, r_3\) are in the ratio \(1: 2: 3\), then its sides are in the ratioAP EAMCET 2018 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
More PYQs from AP EAMCET
- If \(\int_0^{10} f(x) d x=5\), then \(\sum_{k=1}^{10} \int_0^1 f(k-1+x) d x=\)AP EAMCET 2017 Medium
- In the binomial expansion of \((p-q)^{14}\), if the sum of \(7^{\text {th }}\) term and \(8^{\text {th }}\) term is zero, then \(\frac{p+q}{p-q}=\)AP EAMCET 2025 Medium
- The value of \(\lambda\) with \(|\lambda| < 16\) such that \(2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0\) represents a pair of straight lines, isAP EAMCET 2009 Medium
- If a circle \(S\) passing through the point \((3,4)\) cuts the circle \(x^2+y^2=36\) orthogonally, then the locus of the centre of \(S\) isAP EAMCET 2018 Medium
- Match the following
\(\begin{array}{ll}
\text{List - I} & \text{List - II} \\
\text{i) Isothermal process} & \text{a)} 0 \\
\text{ii) Isobaric process} & \text{b)} \frac{1}{\gamma-1}\left[\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1\right] \\
\text{iii) Isochoric process} & \text{c)} \mu \mathrm{RT} \ln \left(\frac{V_2}{V_1}\right) \\
\text{iv) Adiabatic process} & \text{d)} \mathrm{P}\left(\mathrm{V}_2-\mathrm{V}_1\right) \\
\end{array}\)
The correct answer isAP EAMCET 2017 Easy - If \(1, a, a^2, \ldots, a^{n-1}\) are the \(n\)th roots of unity. Then \(\sum_{i=1}^{n-1} \frac{1}{2-a^i}\) is equal toAP EAMCET 2020 Hard