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Let f(x) = { 1-abs(x) , abs(x)le 1 0 ,...

Let f(x) = `{ 1-abs(x) , abs(x)le 1
0 , abs(x) gt 1 ` and g(x) =f(x-1) +f(x+1) `xinR , then value of `int_(-3)^3 g(x) dx` is equal to

A

2

B

3

C

period of h(x) =`sinpix`

D

period of `phi(x) =cos (2pix)`

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The correct Answer is:
A, C
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. If I= int0^(pi/2) dx/(sqrt(1+sin^3x) then

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  2. int0^pi xf(sinx)dx is equal to

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  3. Let f(x) = { 1-abs(x) , abs(x)le 1 0 , abs(x) gt 1 and g(x) =f(x-1)...

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  4. The values of alpha which satisfy int(pi/2)^alpha sin2alpha (alpha in ...

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  5. Let f(x) = int2^x f(t^2-3t+2) dt then

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  6. Let f(x) be a continous function defined on the closed interval [a,b] ...

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  7. Let f(x) be a continous function defined on the closed interval [a,b] ...

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  8. If f(x) be an increasing function defined on [a,b] then max {f(t) alet...

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  9. If f(x) be an increasing function defined on [a,b] then max {f(t) alet...

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  10. Choose the correct answer: The hybridisation of the carbon atom (under...

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  11. Choose the correct answer: The hybridisation of the carbon atom (under...

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  12. If int0^(pi/2) sintheta log sintheta d theta =log (A/(198e)) then the ...

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  13. If int0^1 dx/((1+x)(2+x)(sqrt(x(1-x)))) = (piA)/(sqrt6(sqrt3+1)) then ...

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  14. If-int0^(2pi) [sinx+cosx]dx =Api and [x] denotes the greatest integer ...

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  15. The value of the integral sqrt2 int0^pi sqrt(1-cos2x) dx is ?

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  16. The value of the integral sqrt2 int0^(pi/2) f(sin2x) sinx dx=A (sqrt2/...

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  17. Evaluate int0^sqrt3 (1/(1+x^2)) sin^(-1)((2x)/(1+x^2)) dx

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  18. Evaluate : int0^(pi//2) cos^3xcdot sinx dx

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  19. Evaluate int0^(pi/4) (e^(secx) (sin(x+(pi/4)))/(cosx(1-sinx)) dx

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  20. If absalt1 show that int0^pi (log(1+acosx))/cosx dx= pisin^(-1)a

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