HSC Commerce 12th Board ExamMaharashtra State Board
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# Solution - Evaluate :∫π/2 0 dx/(1+cotx) - HSC Commerce 12th Board Exam - Mathematics and Statistics

#### Question

Evaluate :int_0^(pi/2)dx/(1+cotx)

#### Solution

Let I=int_0^(pi/2)dx/(1+cotx)

 =int_0^(pi/2)dx/(1+(cosx)/(sinx))

=int_0^(pi/2)dx/((sinx+cosx)/sinx)

=int_0^(pi/2)sinx/(sinx+cosx)dx..................(i)

We know

int_0^af(x)dx=int_0^af(a-x)dx

I=int_0^(pi/2)(sin(pi/2-x))/(sin(pi/2-x)+cos(pi/2-x))

I=int_0^(pi/2)cosx/(cosx+sinx)dx.................(ii)

I+I=int_0^(pi/2)sinx/(sinx+cosx)dx+int_0^(pi/2)cosx/(cosx+sinx)dx

2I=int_0^(pi/2)(sinx+cosx)/(sinx+cosx)dx

2I=int_0^(pi/2)1dx=[x]_0^(pi/2)

I=1/2[x]_0^(pi/2)=1/2[pi/2-0]

I=pi/4

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 3.2.2 | 4 marks

#### Video TutorialsVIEW ALL [2]

Solution for question: Evaluate :∫π/2 0 dx/(1+cotx) concept: null - Integration by Parts. For the courses HSC Commerce, HSC Commerce (Marketing and Salesmanship)
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