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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{\operatorname{cosec}^2 x-2022}{\cos ^{2022} x} d x=f(x)+C \Rightarrow f(\pi / 4)=\)

  1. A \(\left(\frac{1}{2}\right)^{1011}\)
  2. B \(-2^{1011}\)
  3. C \(2^{2011}\)
  4. D \(-2^{2022}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-2^{1011}\)

Step-by-step Solution

Detailed explanation

\(I=\int \frac{\operatorname{cosec}^2 x-2022}{\cos ^{2022} x} d x\) \(\begin{aligned} & =\int(\cos x)^{-2022} \cdot \operatorname{cosec}^2 x d x-2022 \int \frac{d x}{\cos ^{2022} x} \\ & =(\cos x)^{-2022} \int \operatorname{cosec}^2 x d x\end{aligned}\)…