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The value overset(2)underset(-2)int {p...

The value
`overset(2)underset(-2)int {p" In"((1+x)/(1-x))+q" In "((1-x)/(1+x))-2+r}dx` depends on the value of

A

the value of p

B

the value of q

C

the value of r

D

The values of p and q

Text Solution

Verified by Experts

The correct Answer is:
C
` l =int_(-2)^(2)[plog((1+x)/(1-x))+qlog((1-x)/(1+x))^(-2)+r]dx`
Since , log `((1+x)/(1-x))` is an odd function .
`rArrint_(-2)^(2)log((1+x)/(1-x))dx=0`
`therefore l = int_(-2)^(2)r dx =r (2+2)=4r`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  2. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  4. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

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  5. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

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  7. int (-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] dx is equalt to

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  8. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  9. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

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  10. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equ...

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  11. The value of the integral int (0)^(pi//2) sin ^(5) x dx is

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  14. The value of int (0)^(pi//2) sin ^(8) x dx is

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  15. The value of overset(pi)underset(-pi)int(1-x^(2)) sin x cos^(2) x" dx"...

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