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

Let f(x) be a function satisfying `f'(x)=f(x)` with `f(0)=1andg(x)` be a function that satisfies `f(x)+g(x)=x^(2)`. Then the value of the integral `int_(0)^(1)f(x)g(x)dx,` is

A

`e + (e^(2))/(2) + 5/2`

B

`e - (e^(2))/(2) - 3/2`

C

`e - (e^(2))/(2) - 5/2`

D

`e + (e^(2))/(2)-3/2`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
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  10. If int(0)^(pi) f(tan x) dx= lambda then int(0)^(2pi) f(tan x) dx=

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  12. Evaluate (i) int(0)^(pi/2) (sin^(2)x)/(sin x + cos x ) dx

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  13. int(0)^(1) Tan^(-1) ((2x-1)/(1+x-x^(2)))dx=

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  14. int(0)^(oo) (ln x)/(x^(2)+a^(2))dx=

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  15. int(0)^(pi//2) ln (tan x+ cot x)dx=

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  16. Evaluate the integral underset(0)overset(1)int (log(1+x))/(1+x^(2))d...

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  17. int(0)^(2pi) ln (1+Cos x) dx=

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  18. int(0)^(pi//2) (sin 8x.log(cot x))/(cos 2 x)dx=

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  19. int(0)^(4014) (2^(x))/(2^(x) +2^(4041-x))dx=

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  20. int(0)^(pi//2) (1)/(1+e^(sqrt(2)sin(x-pi//4)))dx=

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