TS EAMCET · Maths · Definite Integration
\(\int_0^{2 \pi} \sin ^6 x \cos ^5 x d x\) is equal to
- A \(2 \pi\)
- B \(\pi / 2\)
- C \(0\)
- D \(-\pi\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
Let \(\begin{aligned} I & =\int_0^{2 \pi} \sin ^6 x \cos ^5 x d x \\ I & =2 \int_0^\pi \sin ^6 x \cos ^5 x d x\end{aligned}\) \([\because f(2 \pi-x)=f(x)]\) Let \(f(x)=\sin ^6 x \cos ^5 x\) \([\because f(\pi-x)=-f(x)]\)…
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 \(X\) is a poisson variate with \(P(X=0)=0.8\), then the variance of \(X\) isTS EAMCET 2004 Easy
- If \(x^2+2 p x-2 p+8>0\) for all real values of \(x\), then the set of all possible values of \(p\) isTS EAMCET 2023 Easy
- The equation of a line making an angle \(60^{\circ}\) with the line \(x+y-3=0\) and passing through the point \((1,1)\) isTS EAMCET 2020 Easy
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-9 x^2+23 x-15=0\), then \(\alpha^3+\beta^3+\gamma^3=\)TS EAMCET 2022 Medium
- The value of is equal toTS EAMCET 2020 Medium
- Consider the four points \(A(1,-2,-1)\), \(B(4,0,-3), C(1,2,-1)\) and \(D(2,-4,-5)\) in space. If \(\mathbf{b}=\mathbf{A B}, \mathbf{c}=\mathbf{A C}\) and \(\mathbf{d}=\mathbf{A D}\), thenTS EAMCET 2021 Hard
More PYQs from TS EAMCET
- Let \(\overrightarrow{\mathbf{a}}\) be a unit vector, \(\overrightarrow{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=\hat{\mathbf{i}}+3 \hat{\mathbf{k}}\). Then, maximum value of \([\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]\) isTS EAMCET 2008 Easy
- At very high frequencies, the current (i) in the given circuit is
TS EAMCET 2023 Hard - The solution of the differential equation , isTS EAMCET 2019 Easy
- The relation between the displacement ' \(x\) ' (in metre) and the time ' \(t\) ' (in second) of a particle is \(\mathrm{t}=2 x^2+3 x\). If the displacement of the particle is 25 cm from the origin \((x=0)\), then the acceleration of the particle isTS EAMCET 2025 Medium
- When a body of mass \(1.0 \mathrm{~kg}\) is suspended from a certain light spring hanging vertically, its length increases by \(5 \mathrm{~cm}\). By suspending \(2.0 \mathrm{~kg}\) block to the spring and if the block is pulled through \(10 \mathrm{~cm}\) and released, the maximum velocity in it in \(\mathrm{m} / \mathrm{s}\) is : (Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\) )TS EAMCET 2003 Medium
- For , if , thenTS EAMCET 2020 Medium