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Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x...

Let `inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot` Then `inte^xf(x)dx` is

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
Here, `int e^(x){f(x)-f'(x)}dx=phi(x)`
and `int e^(x){f(x)+f'(x)}dx=e^(x)f(x)`
On adding, we get `2int e^(x)f(x)dx=phi(x)+e^(x)f(x)`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  2. If In=int( lnx)^n dx then In+nI(n-1)

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  3. Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is

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  4. For x >1,int sin^(- 1)((2x)/(1+x^2))dx is equal to

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  5. If int(xln(x+sqrt(1+x^2)))/(sqrt(1+x^2))dx =asqrt(1+x^2)ln(x+sqrt(1+x...

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  7. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  8. Find the value of " int x sec^(2)x dx

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  9. int x sinx sec^(3)x dx is equal to

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  10. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

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  11. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx is equal to (a)e^xtan(pi/4-x...

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  13. The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)...

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  14. int e^x((x^2+1))/((x+1)^2)dx is equal to (a) ((x-1)/(x+1))e^x+c (b)...

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  15. int((x+2)/(x+4))^2 e^xdx is equal to

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  16. inte^(tanx)(secx-sinx)dxi se q u a lto e^(tanx)cosx+C e^(tanx)sinx...

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  17. int(cos e c^2x-2005)/(cos^(2005)x)dx is equal to (a) -(cotx)/((cosx)^...

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  18. int(1+2x^(2)+(1)/(x))e^(x^(2)-(1)/(x))dx is equal to (a) -x e^(x^(2)...

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  19. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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  20. If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x)...

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