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int (-1)^(1) (e^(x^(3)) +e^(-x^(3))) (e...

` int _(-1)^(1) (e^(x^(3)) +e^(-x^(3))) (e^(x)-e^(-x)) dx` is equal to

A

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

B

` e^(2) - 2e`

C

` (e^(2)-2e)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x)=(e^(x^(3))+e^(-x^(3)))(e^(x)-e^(-x))`
`rArrf(-x)=(e^(-x^(3))+e^(x^(3)))(e^(-x)-e^(x))`
`=-(e^(x^(3))+e^(-x^(3)))(e^(x)-e^(-x))=-f(x)`
`rArr`f(x) is an odd function.
`thereforeint_(-1)^(1)f(x)dx=0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. The value of int (1)^(2) (dx)/((x+1) sqrt((x^2)-1)) is

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  2. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

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  3. int (-1)^(1) (e^(x^(3)) +e^(-x^(3))) (e^(x)-e^(-x)) dx is equal to

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  4. underset(n to oo)lim((1)/(n)+(1)/(n+1)+...+(1)/(3n)) is equal to

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  5. Let f (x) = x – [x], for every real number x, where [x] is the greates...

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  6. The value of int (0)^(1) (x^(4) +1)/(x^(2)+1)dx is

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  7. The value of overset(5)underset(3)int (x^(2))/(x^(2)-4)dx, is

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  8. The value of int (0)^(pi//2) ((sin x + cos x)^(2))/(sqrt(1+sin 2x) dx...

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  9. int (0)^(a) sqrt(a^(2) - x^(2)) dx is equal to

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  10. The value of int(e^(-1))^(e) (dt)/(t(t+1)) is equal to

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  11. The value of int (1)^(e) 10^(log(e)x) dx is equal to

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  12. If int (2)^(e) (1/(logx)-1/(logx)^(2))dx = a + b/(log2) , then

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  13. int (0)^(oo) (dx)/((x+ sqrt(x^(2)+1))^(3)) is equal to

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  14. The value of the integral int (-pi//2)^(pi//2) sqrt(cos x - cos ^(3) ...

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  15. The value of I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(...

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  16. int (alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

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

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  18. The value overset(2)underset(-2)int {p" In"((1+x)/(1-x))+q" In "((1-...

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  19. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

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  20. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

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