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about to only mathematics...

about to only mathematics

A

`pi`

B

`1`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int_(0)^(pi) e^(cos^(2)x)cos^(3)(2n+1)x dx, n epsilonZ` …………..1
`=int_(0)^(pi) e^(cos^(2)(pi-x))cos^(3)[(2n+1)(pi-x)]dx`
[Using `int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx`]
`=int_(0)^(pi)e^(cos^(2)x)cos^(3)[(2n+1)pi-(2n+1)x]dx`
`=-int_(0)^(pi)-e^(cos^(2)x)cos^(3)(2n+1)xdx`
`=-I`
or `I=0`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. "I f"I1=int(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I2=int(-10...

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  2. The value of int0^oo(x dx)/((1+x)(1+x^2)) is equal to

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  3. about to only mathematics

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  4. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)]dx , I2=i...

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  5. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I2=int(f...

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  6. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

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

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  8. f(x)>0AAx in Ra n di sbou n d e ddotIf (lim)(nvecoo)[int0^a(f(x)dx)/...

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

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  10. The value of the definite integral int0^1(1+e^-x^2)dx (b) 2 1+e^...

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

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

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

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

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

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

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

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

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

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

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