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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)
  1. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is sqrt(...

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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 int0^1(1+e^-x^2)dx (b) 2 1+e^...

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  5. T h ev a l u eoft h ein t egr a lint(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(...

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  6. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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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. Evaluate int(0)^(pi/2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx

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  9. For x in R and a continuous function f, let I1=int(s in^2t)^(1+cos^2t...

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

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  11. The value of the definite integral int2^4x(3-x)(4+x)(6-x)(10-x)+sinx)d...

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  12. IfI=int(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot] denotes the greate...

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  13. Which of the following statement is always true? (a)If f(x) is increas...

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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=

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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. Evaluate int(0)^(1)(x^2/(1+x^2))dx

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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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