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if f(x)=-int0^xlog(cost)dt, then the val...

if `f(x)=-int_0^xlog(cost)dt`, then the value of `f(x)-2f(pi/4+x/2)+2f(pi/4-x/2)` is equal to

A

(-xlog2)

B

`x/2log2`

C

` x/3 log2`

D

none of these

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A
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
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  3. if f(x)=-int0^xlog(cost)dt, then the value of f(x)-2f(pi/4+x/2)+2f(pi/...

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  6. The value of x satisfying int0^(2[x+14]){x/2}dx=int0^({x})[x+14]dxis e...

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  7. if ngt1and I=int0^infty dx/((x+sqrt(1+x^2))^n then I equals

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  8. If [x] denotes the greatest integer lex and n inN then value of In=int...

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  9. if I=int0^1dx/((1+x)(2+x)sqrtx(1-x)then I equals

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  10. if int0^1 x(1-x)^(2007//2)dx then it equals

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  11. if I=int(-1)^2abs(xsinpix)dx then I equals

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  12. if I=int(alpha)^(beta)[loglogx+1/(logx)^2]dx then I equals

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  13. if I=int0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I eq...

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  14. if 0ltalphalt1 and I=int(-1)^1dx/(sqrt(1-2alphax+alpha^2) then I equal...

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  15. if I=int8^15 dx/((x-3)sqrt(x+1)) then I equals

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  16. underset(xrarr(pi//4))lim( int2^(sec^2x)(f(t)dt))/(x^2-(pi)^2/16 equal...

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  17. If int1^infty((x^3+3)dx)/(x^6(x^2+1))=(a+bpi)/c, then

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  18. If int0^1 ((1-x^2)dx)/(1+x^2+x^4) =aInb then,

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  19. If f(x)=int(-2)^xabs(t+1)dt then,

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  20. Let f(x)be a function satisfying f(x)=f(x) with f(0)=1 and 'g' be the ...

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