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If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ...

If `f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}`. Then `int_-2^3 f(x)dx=`______

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`I=underset(-2)overset(3)intf(x)dxunderset(-2)overset(3)int e^(cosx) sin x dx + underset(2)overset(3)int 2 dx`
`rArr I=0+2(3-2)[ {:( :., g(x) =e^(cosx) "sin x is an odd function"),( :., underset(-2)overset(2)int (x) dx=0):}]`
`rArr I=2`
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
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  2. If f(x) is a function satisfying f((1)/(x))+x^(2)f(x)=0 for all non ...

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  3. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

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  4. The value of the integral int (e ^(-1))^(e ^(2))|(ln x )/(x)|dx is:

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  5. about to only mathematics

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  6. Let f: (0, infty) rarr R and F (x) = int(0) ^(x) f(t) dt . If F(x^(2)...

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  7. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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  8. Let T >0 be a fixed real number. Suppose f is continuous function such...

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  9. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation x^...

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  10. If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int(1//x)^(x) f(t)dt, (1)/(...

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  11. If | int(a)^(b) f(x)dx|= int(a)^(b)|f(x)|dx,a ltb,"then " f(x)=0 has

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  12. Let f(x) be an odd continous function which is periodic with period 2....

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  13. All the value of d for which int(1)^(2){a^(2)+(4-4a)x+4x^(3)} d xle1...

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  14. Let f(x) be a function defined by f(x)=int(1)^(x)t(t^(2)-3t+2)dt,1ltxl...

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  15. If int(0)^(x){t}dt=int(0)^({x})t dt ("where" x gt0 neZ and and {*} rep...

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  16. Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer l...

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  17. rArrint(0)^(oo) [(2)/(e^(x))]dx (where [*] denotes the greatest intege...

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  18. Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...

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  19. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

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  20. For x epsilonR, and a continuous function f let I(1)=int(sin^(2)t)^(1+...

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