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Let f(x) be a function satisfyingf'(x)=f...

Let f(x) be a function satisfying`f'(x)=f(x)` with`f(0) =1` and g(x) be a function that satisfies `f(x) + g(x) = x^2` . Then 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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FIITJEE-DEFINITE INTEGRAL -ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-I)
  1. If int(0)^(1)(ax+b)/(x^(2)+3x+2)dx=ln.(3)/(2), then

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  2. If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int(0)^(1)f(x)phi(x)dx is

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  3. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  4. int(0)^(alpha)(1)/(cosx+cosalpha)dx is equal to

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  5. If int(-pi//4)^(3pi//4)(e^(pi//4)dx)/((e^(x)+e^(pi//4))(sinx+cosx))=ki...

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  6. The value of int(0)^(2pi)|cosx-sinx|dx is equal to

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  7. int(0)^(pi//2)(dx)/(1+e^(sqrt(2)cos(x+(pi)/(4)))) is equal to

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  8. int(0)^(pi//2n)(dx)/(1+(cotnx)^(n)) is equal to (ninN)

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  9. The value of int(0)^(4pi)|sinx|-[(|sinx|)/(2)]-[(|cosx|)/(2)]dx is

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  10. If f((1)/(x))+x^(2)f(x)=0,AAxgt0 then int(sinx)^(cosecx)f(z)dz is for ...

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  11. The value of the integral int(pi//6)^(pi//3)(dx)/(1+tan^(5)x) is

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  12. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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  13. The value of int(0)^(pi//2)ln((sin^(2)theta)/(cos^(3)theta))d theta is

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  14. int(-1)^(1)[tan^(-1){sin(cos^(-1)x)}+cot^(-1){cos(sin^(-1)x)}dx=

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  15. int- 8^8(sin^(93)x+x^(295))\ dx

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  16. Let I=int0^1(sin)/(sqrt(x))dx"and"J=int0^1(cosx)/(sqrt(x))dx Then w...

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  17. int0^100 {sqrtx} dx (where {x) is fractional part of x ) =

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  18. int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=

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  19. If bgta, then int(a)^(b)(dx)/(sqrt((x-a)(b-x))) is equal to

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  20. inta^bsqrt((x-a)(b-x)) dx , a > b

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