1. Tardigrade
  2. Question
  3. Mathematics
  4. Statement II f (d/d x)(- operatornamecosec x)= operatornamecosec x cot x, then ∫ operatornamecosec x cot x d x=- operatornamecosec x+C Statement II If we know the formulae for the derivative of many important functions, then we can write down the corresponding formulae for the integrals of these functions.

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Q. Statement II f $\frac{d}{d x}(-\operatorname{cosec} x)=\operatorname{cosec} x \cot x$, then $\int \operatorname{cosec} x \cot x d x=-\operatorname{cosec} x+C$
Statement II If we know the formulae for the derivative of many important functions, then we can write down the corresponding formulae for the integrals of these functions.

Integrals

Solution:

It is correct to say that we can write the corresponding formulae tor the integrals of the functions it we know the formulae of its derivatives.
$\therefore \text { If } \frac{d}{d x}(-\operatorname{cosec} x)=\operatorname{cosec} x \cot x \text {, then }$
$\int \operatorname{cosec} x \cot x d x=-\operatorname{cosec} x+C$