Karnataka Board PUCPUC Science 2nd PUC Class 12

Write a Value of ∫ Tan X Sec 3 X D X - Mathematics

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Sum

Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]

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Solution

Let I=\[\int\]tan x . sec3x dx

      =\[\int\]sec2 x . sec x tan x dx

Let sec x = t
⇒ sec tan x dx = dt

\[\therefore I =  ∫ t^2 dt      \]
\[= \frac{t^3}{3} + C\]

\[ = \frac{\sec^3 x}{3} + C \left( \because x = \sec x \right)\]

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Chapter 19: Indefinite Integrals - Very Short Answers [Page 197]

APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 14 | Page 197

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