Question Bank - Mathematics

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What is the value of \(\rm \int \frac{sec^2x}{cosec^2x} \ dx\)

A.
tanx - x + C
B.
cotx + x + C
C.
tanx + x + C
D.
cotx - x + c

Solution:

Concept:Some useful formulas are:\(\rm \frac{1}{cos^2x} = sec^2x\)\(\rm \frac{1}{sin^2x} = cosec^2x\)\(\rm? sec^2x \ dx = tanx + C\)\(\rm? dx = x + C\)Calculation:\(\rm ? \frac{sec^2x}{cosec^2x} \ dx\)? \(\rm ? \frac{\frac{1}{cos^2x}}{\frac{1}{sin^2x}} \ dx\)? \(\rm ? {sin^2x \over cos^2x} \ dx\)? \(\rm ? tan^2x \ dx\)? \(\rm ? (sec^2x-1) \ dx\)? \(\rm? sec^2x \ dx -? dx\)? tanx - x + C, where C is the constant of integration

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