HSC Commerce (Marketing and Salesmanship) 12th Board ExamMaharashtra State Board
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# Evaluate : ∫ 2 1 1 ( X + 1 ) ( X + 3 ) D X - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

#### Question

Evaluate : int_1^2 1/((x+1)(x+3)) dx

#### Solution

int_1^2 1/((x+1)(x+3)) dx

= 1/2int_1^2(1/(x+1)-1/(x+3))dx

=1/2[{log(x+1)}_1^2-{log(x+3)}_1^2]

=1/2[(log)3-log2)-(log 5-log4)]

=1/2(log3+log4)-(log2+log5)

=1/2[log12-log10]

=(1/2)log (12/10)

∴int_1^2 1/((x+1)(x+3))dx=1/2 log (6/5)

Is there an error in this question or solution?

#### APPEARS IN

2017-2018 (March) (with solutions)
Question 3.2.3 | 4.00 marks
Solution Evaluate : ∫ 2 1 1 ( X + 1 ) ( X + 3 ) D X Concept: Maxima and Minima.
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