AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\operatorname{cosec}^2 x-2022}{\cos ^{2022} x} d x=f(x)+C \Rightarrow f(\pi / 4)=\)
- A \(\left(\frac{1}{2}\right)^{1011}\)
- B \(-2^{1011}\)
- C \(2^{2011}\)
- D \(-2^{2022}\)
Answer & Solution
Correct Answer
(B) \(-2^{1011}\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{\operatorname{cosec}^2 x-2022}{\cos ^{2022} x} d x\) \(\begin{aligned} & =\int(\cos x)^{-2022} \cdot \operatorname{cosec}^2 x d x-2022 \int \frac{d x}{\cos ^{2022} x} \\ & =(\cos x)^{-2022} \int \operatorname{cosec}^2 x d x\end{aligned}\)…
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 lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\), isAP EAMCET 2008 Easy
- The number of four-digit numbers formed by using the digits \(0,2,4,5\) and which are not divisible by 5 , isAP EAMCET 2015 Medium
- Let and be roots of the equation and let and be the roots of the equation If are in then and areAP EAMCET 2021 Easy
- Maximum area of the rectangle that can be formed with the fixed perimeter ' \(p\) ' \(\mathrm{cm}\)AP EAMCET 2020 Easy
- The direction cosines of the line passing through \(P(2,3-1)\) and the origin areAP EAMCET 2005 Easy
- Find the transformed equation of the curve \(x^2+2 \sqrt{3} x y-y^2=8\), when the axes are rotated through an angle \(\frac{\pi}{3}\).AP EAMCET 2021 Hard
More PYQs from AP EAMCET
- Let \(B=\left(\begin{array}{ccc}2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & 1 & -1\end{array}\right)\) and \(C=\left(\begin{array}{ccc}-1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2\end{array}\right)\)
If a matrix \(A\) is such that \(\mathrm{BAC}=\mathrm{I}\), then \(\mathrm{A}^{-1}=\)AP EAMCET 2023 Easy - Calculate the de-Broglie's wavelength of an electron residing in the 2nd Bohr's orbit of a hydrogen atom. (Bohr's radius, \(a_0=0.529 Å\) )AP EAMCET 2021 Medium
- Two resistances are connected in the two gaps of a meter bridge. The balancing point is obtained at \(20 \mathrm{~cm}\). When a resistance of \(15 \Omega\) is connected in series with the smaller resistance of the two, the balancing point shifts to \(40 \mathrm{~cm}\). The value of smaller resistance isAP EAMCET 2023 Easy
- The equation of radical axis of the circles and isAP EAMCET 2021 Medium
- \(\int \frac{(3 x-2) \tan \left(\sqrt{9 x^2-12 x+1}\right)}{\sqrt{9 x^2-12 x+1}} d x=\)AP EAMCET 2025 Medium
- If \(7 \cos \theta-\sin \theta=5\) and \(\tan \theta>0\), then \(\tan \theta=\)AP EAMCET 2025 Medium