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Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1...

`Ifint_0^1cot^(-1)(1-x+x^2)dx=lambdaint_0^1tan^(-1)x dx ,t h e nlambdai se q u a lto` 1 (b) 2 (c) 3 (d) 4

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(0)^(1)cot^(-1)(1-x+x^(2))dx`
`=int_(0)^(1)tan^(-1)(1/(1-x+x^(2)))dx`
`=int_(0)^(1)tan^(-1)((x+(1-x))/(1-x(1-x)))dx`
`=int_(0)^(1)tan^(-1)x dx+int_(0)^(1)tan^(-1)(1-x)dx`
`=int_(0)^(1)tan^(-1)x dx+int_(0)^(1)tan^(-1)[1-(1-x)]dx`
`=2int_(0)^(1)tan^(-1)xdx` or `lamda=2`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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  2. f(x)>0AAx in Ra n di sbou n d e ddotIf (lim)(nvecoo)[int0^a(f(x)dx)/...

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  3. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,t h e nlambdai s...

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  4. The value of the definite integral int(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)...

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  5. The value of the integral int(-3pi//4)^(5pi//4)((sinx+cosx))/(e^(x-pi/...

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  6. I(1)=int(0)^((pi)/2)In (sinx)dx, I(2)=int(-pi//4)^(pi//4)In(sinx+cosx)...

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  7. IfI1=int0^(pi/2)(cos^2x)/(1+cos^2x)dx ,I2=int0^(pi/2)(sin^2x)/(1+sin^2...

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  8. int0^(pi/2) (xsinxcosx)/(cos^4x+sin^4x) dx=

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

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  10. Ifint(-pi)^((3pi)/4)(e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx)=kint(-pi/2...

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  11. The value of the definite integral int(2)^(4)(x(3-x)(4+x)(6-x)(10-x)+s...

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  12. If I=int(-20pi)^(20pi)|sinx|[sinx]dx (where [.] denotes the greatest i...

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  13. The function f and g are positive and continuous. If f is increasing a...

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  14. int(0)^(pi)(x tanx)/(secx+cosx)dx is

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  15. If f(x)=int(0)^(pi)(t sin t dt)/(sqrt(1+tan^(2)xsin^(2)t)) for 0lt xlt...

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  16. int(-3)^(3)x^(8){x^(11)}dx is equal to (where {.} is the fractional pa...

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  17. The value of int(0)^(4pi)log(e)|3sinx+3sqrt(3) cos x|dx then the value...

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  18. The value of int(0)^(pi)(|x|sin^(2)x)/(1+2+cosx|sinx)dx is equal to

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  19. The value f the integral int(-pi)^pisinm xsinn xdx , for m!=n(m , n in...

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  20. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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