HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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Solution - Integrate : sec^3x w. r. t. x. - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

Question

Integrate : sec3 x w. r. t. x.

Solution

`I = intsec^3x dx`

`I =int secx.sec^2x dx`

`I =secx.intsec^2xdx-int[d/dx(secx).int sec^2x dx] dx`

`I =secx.tanx-int secx.tanx.tanx dx`

`I =secx.tanx-int secx(sec^2x -1)dx`

`I =secx.tanx-int [sec^3x-secx]dx`

`I =secx.tanx-int sec^3x + int secxdx`

`I =secx.tanx - I + log|secx + tanx| + c`

`2I =secx.tanx + log|secx + tanx| + c`

`therefore I =1/2(secx.tanx + log|secx + tanx|) + c`

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 5.1.1 | 3 marks

Video TutorialsVIEW ALL [1]

Reference Material

Solution for question: Integrate : sec^3x w. r. t. x. concept: Methods of Integration - Integration by Parts. For the courses HSC Science (Electronics), HSC Science (Computer Science), HSC Science (General) , HSC Arts
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