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int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c...

`int_(-pi/2)^(pi//2) log_(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx`is equal to

A

`pi log_(e )(a+b)`

B

`pi log_(e )((a+b)/(2))`

C

`(pi)/(2)log_(e )(a+b)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is

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  2. int(1)^(-1) (x^(3)+|x|+1)/(x^(2)+2|x|+1)dxis equal to

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  3. int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...

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  4. For any natural number n, the value of the integral int(0)^(sqrt(n))...

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  5. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

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  6. If phi'(x)=(log(e )|sin x|)/(x),x ne pi,n in Z and int(1)^(3) (3log(...

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  7. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

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  8. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...

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  9. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

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  10. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

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  11. If [.] denotes the greatest integer function and f(x)={:{(3[x]-(5|x|...

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  12. Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...

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  13. The value of int(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int(-1)^(1) cos^(-...

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  14. Let Delta(y)=|{:(y+a,y+b,y+a-c),(y+b,y+c,y-1),(y+c,y+d,y-b+d):}| and,...

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  15. If I=int0^(1) (1)/(1+x^(pi//2))dx, then\

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  16. If int(0)^(x) f(t)dt=x^(2)+2x-int(0)^(x) tf(t)dt, x in (0,oo). Then, f...

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  17. The value of int(-6)^(6) "max"(|2-|x||,4-|x|,3)dx ,is

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  18. If I(n)=int(0)^(pi) e^(x)(sinx)^(n)dx, then (I(3))/(I(1)) is equal to

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  19. Given that lim(n to oo)sum(r=1)^(n)(log(n^(2)+r^(2))-2logn)/(n)=log2...

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  20. Let f(x)be a differentiable function such that f'(x)=f(x)+int(0)^(2)...

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