Past paper 1995
∫(2x)(√(x^2 + 1) ) dx
=?
i can't "In" this equation, i saw the past paper making, but i don't understand.
please don't use "let u = x^2 + 1" , i don't understand this method.
thank you.
A.math Indefinite Integrals
2009-12-22 12:23 am
回答 (2)
2009-12-22 6:34 am
✔ 最佳答案
y = ∫ 2x√(x^2 + 1) dx= 2(1/2)∫√(x^2 +1)dx^2
= ∫√(x^2 + 1) d(x^2 +1)
y = (2/3)(x^2 + 1)^(3/2) + c
when x =0,y =1
1 = 2/3 + c
c =1/3
the equation is y = (2/3)(x^2 +1)^(3/2) + (1/3)
2009-12-22 1:58 am
I think this Q is out C. Integration by substitution is no longer in current A-maths syllabus. For this Q, the only approach is integration by substitution(letting u equals sth), so an alternative is not available. So you may simply ignore this Q.
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