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

ConceptMethods of Integration - Integration by Parts

#### 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

Is there an error in this question or solution?

#### APPEARS IN

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

#### 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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