31)sin-1x+cos-1x=pi/2 it was an identity.
2) take cases when n is an even or odd,while x is positive or negative
Ques1) Solve ∫ √ (x-3 ) { Sin -1(ln x) + cos -1 (ln x) } dx
(a) (x-3) 3/2 + c (b) 0 (c) does not exists (d)none of these
Ques2) Show that , if n is an odd positive integer, then ∫ |x n | dx equals to (|x n| x ) / (n+1) + C
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8 Answers
3
24@msp..
sin-1x+cos-1x=Ï€2
here x ε[-1,1]
and lnx is mapped from (0,∞)→R
11I got the first one correct.
Ans is (c)
Plzzz someone solve the second.
1When x is positive,
∫|xn|=∫xn=x(n+1)/(n+1)=|xn|x/n+1 where x is -ve
When x is negative,
Clearly xn is negative when x is -ve, since n is odd.......
∫|xn|=-∫xn=-x(n+1)/(n+1)=|xn|x/n+1 where x is -ve
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3ya eure the same wat i told eure i want u to split the integrand so its definitely defined and it is not a) and also it is not defined na.
