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# Solution - Prove that ∫√(x^2-a^2)dx=x/2 √(x^2-a^2)-a^2/2 log|x+√t(x^2-a^2)|+c - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

ConceptMethods of Integration - Integration by Parts

#### Question

Prove that int sqrt(x^2-a^2)dx=x/2sqrt(x^2-a^2)-a^2/2log|x+sqrt(x^2-a^2)|+c

#### Solution

Let  I=int sqrt(x^2-a^2)dx

I=int sqrt(x^2-a^2).1.dx

I=sqrt(x^2-a^2).intdx -int[d/dx(sqrt(x^2-a^2))intdx]dx

I=xsqrt(x^2-a^2)-int[(2x)/(2sqrt(x^2-a^2))x]dx

I=xsqrt(x^2-a^2)-int[(x^2)/(sqrt(x^2-a^2))]dx

I=xsqrt(x^2-a^2)-int[(x^2-a^2+a^2)/(sqrt(x^2-a^2))]dx

I=xsqrt(x^2-a^2)-int(x^2-a^2)/(sqrt(x^2-a^2))dx+a^2intdx/(sqrt(x^2-a^2)

I=xsqrt(x^2-a^2)-intsqrt(x^2-a^2)dx+a^2intdx/(sqrt(x^2-a^2)

I=xsqrt(x^2-a^2)-I+a^2intdx/(sqrt(x^2-a^2)

2I=xsqrt(x^2-a^2)+a^2log|x+sqrt(x^2-a^2)|+C'

I=(xsqrt(x^2-a^2))/2+a^2/2log|x+sqrt(x^2-a^2)|+C^'/2

I=(xsqrt(x^2-a^2))/2+a^2/2log|x+sqrt(x^2-a^2)|+C

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 5.2.2 | 4 marks
2013-2014 (March) (with solutions)
Question 6.2.2 | 4 marks

#### Reference Material

Solution for question: Prove that ∫√(x^2-a^2)dx=x/2 √(x^2-a^2)-a^2/2 log|x+√t(x^2-a^2)|+c concept: Methods of Integration - Integration by Parts. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Science (Electronics), HSC Arts
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