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If f(x)={(e^(cosx)sinx,; |x|le2),(2,; ot...

If `f(x)={(e^(cosx)sinx,; |x|le2),(2,; otherwise):},` then `int_-2^3f(x)dx=`

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0

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3

Text Solution

Verified by Experts

The correct Answer is:
C
`int _(-2)^(3) f(x) dx = int _(-2)^(2) f(x) dx + = int _(2)^(3) f(x) dx `
` int _(-2)^(2) e^(cosx) sin x dx + int _(2)^(3) f(x) 2 dx `
Function of ist integral is an odd function , therefore the value of ist integral is zero
`:. int _(-2)^(3) f(x)dx = 0+2 [ x] _(2)^(3) = 0+2(3-2) =2 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  7. int(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

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  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

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  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

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  11. Which of the following is true ?

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  15. The value of int0 ^(pi/2) (cos3x+1)/(cosx - 1) dx is equal to

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  16. The value of underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx ...

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  17. If f is a continous function, then

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  18. The value of int(-pi)^(pi) sin^(3) x cos^(2) x dx is equal to

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  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

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  20. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

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  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

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