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int(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1...

`int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto` `(sqrt(e))/2(sqrt(3)+1)` (b) `(sqrt(3e))/2` `sqrt(3e)` (d) `sqrt(e/3)`

A

`(sqrt(e))/2(sqrt(3)+1)`

B

`(sqrt(3e))/2`

C

`sqrt(3e)`

D

`sqrt(e/3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`int_(-1)^(1//2)(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2)))=int_(-1)^(1//2)(e^(x)(1-x^(2)+1))/((1-x)sqrt(1-x^(2)))`
`=int_(-1)^(1//2) e^(x)[(sqrt(1+x))/(1-x)+1/((1-x)sqrt(1-x^(2)))]dx`
`=e^(x)sqrt(1+x)/(1-x)|_(-1)^(1//2)=sqrt(3e)`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. about to only mathematics

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  2. Which of the following is incorrect ?

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  3. int(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto (sqrt(e)...

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  4. Ifint(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto" (a)4 (b)...

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  5. int(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to (a) pi/6 (b) (2pi...

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  6. If f(x) is integrable over [1,2] then int(1)^(2)f(x)dx is equal to

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  7. int(e^x)/(e^(2x)+4)dx

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  8. The value of the integral int0^1(dx)/(x^2+2xcosalpha+1) is equal to si...

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  9. int0^oo(dx)/([x+sqrt(x^2+1)]^3)i se q u a lto 3/8 (b) 1/8 (c) -3/8 ...

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  10. Iff(y)=e^y ,g(y)=y;y>0,a n dF(t)=int0^t f(t-y)g(y) dy,t h e n a) F(t...

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  11. Let p(x) be a real polynomial of least degree which has a local maximu...

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  12. The numbers of possible continuous f(x) defined in [0,1] for which I1...

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  13. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

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  14. int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to...

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  15. Evaluate the definite integrals int(0)^((pi)/(4))(sinx+cosx)/(9+16s...

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  16. int(1)^(2)x^(2)dx is equal to

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  17. int(0)^((pi)/(2)) sin^7 xdx is :

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  18. The range of the function f(x)=int(-1)^1(sinxdt)/((1-2tcosx+t^2)i s [...

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  19. If the function f:[0,8]vecR is differentiable, then for 0<a , b<2,int0...

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  20. If f(x)=xtan^(-1)x, then f'(1) is

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