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Let f(x)be a function satisfying f(x)=f(x) with f(0)=1 and 'g' be the function satisfying `f(x)=g(x)=x^2` the value of the integral `int_0^1f(x)g(x)dx` is

A

1/4(e-7)

B

1/4(e-2)

C

1/2(e-3)

D

none of these

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The correct Answer is:
D
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
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  2. If f(x)=int(-2)^xabs(t+1)dt then,

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

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  4. Let In=int0^(pi/4)tan^nxdx, then 1/(I2+I4),1/(I3+I5), 1/(I4+I6), 1/(I5...

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  5. The maximum and minimum values of the integral int0^(pi/2)dx/(1+sin^2x...

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  6. Let f(x)=int0^xabs(sint)dt, then

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  7. The value of int(pisinmxsinnxdx(m,ninN) is equal to for limits-pi to p...

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  8. The value of int(1/e)^tanx(tdt)/(1+t^2)+int(1/e)^cotxdt/(t(1+t^2) is

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  9. If (2x)/piltsinxltx for 0ltxlt(pi/2), the the value of the integral in...

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  10. Definite integral of any discontinuous or non differentiable function ...

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  11. Definite integral of any discontinuous or non diffrentiable function i...

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  12. if m and M are the smallest and greatest values of a function f(x)defi...

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  13. if m and M are the smallest and greatest values of a function f(x) def...

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  14. let F(x)=int0^x(2t div1)/(t^2-2t+2)dt,x in[-1,1] then

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  16. I=int0^2x[2x]dx where [.] denotes the greatest integer function then t...

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  17. If pi/2ltalphalt(2pi)/3 and I=int 0^(sin2alpha)dx/sqrt(4cos^2alpha-x^2...

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  18. if int0^(x^2(1+x))f(t)dt=x then the value of 10f(2) must be

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  19. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

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  20. int(-pi//4)^(pi//4) (sec^2xdx)/(1+e^x)

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