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Let inte^(x){f(x)-f'(x)}dx=phi(x). then...

Let `inte^(x){f(x)-f'(x)}dx=phi(x)`. then, `inte^(x)f(x)dx` is equal to

A

`phi(x)+e^(x)f(x)`

B

`phi(x)-e^(x)f(x)`

C

`(1)/(2){phi(x)-e^(x)f'(x)}`

D

`(1)/(2){phi(x)+e^(x)f'(x)}`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that `inte^(x){f(x)+f'(x)}dx=e^(x)f(x)` It is given that
`int e^(x){f(x)-f'(x)}dx=phi(x)`
Adding these two , we get
`2inte^(x)f(x)dx=phi(x)+e^(x)f(x)`
`rArrinte^(x)f(x)dx=(1)/(2){phi(x)+e^(x)f(x)}`
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
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  2. int secx/(sqrt(sin(2x+alpha)+sinalpha))dx

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  4. If int1/(x+x^5)dx=f(x)+c ,then evaluate int(x^4)/(x+x^5)dxdot

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  5. If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

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  6. If n is a positive odd integer, then int |x^n| dx=

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  7. If inte^(ax)cosbx dx=(e2x)/(29)f(x)+C , then f'' (x)=

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  8. int(sin^(4)x)/(sin^(4)x+cos^(4)x)dx is equal to

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  9. If intf(x)dx=2 {f(x)}^(3)+C , then f (x) is

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  10. Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x)...

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  11. If intg(x)dx=g(x), then the value of the integral intf(x)g(x){f(x)+2...

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  12. If int(1)/(1-sin ^(4)x)dx=(1)/(2) tanx+Atan^(-1){f(x)}+C, then

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  13. intsin2xlog(e)cosx dx is equal to

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  14. Let f(x) be a polynomial of degree three f(0) = -1 and f(1) = 0. Also,...

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  15. int(1)/(x(1+root(3)(x))^(2))dxis equal to

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  16. Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

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  17. Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) t...

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  18. If int(1)/((x+1)(x-2))dx=Alog(e)(x+1)+Blog(e)(x-2)+C , then A + B = ?

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  19. int(x^(4)+1)/(x^(6)+1)dx is equal to

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  20. int(x^(2-1))/(xsqrt(x^4+3x^2)+1)dx is equal to

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