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Prove that: In=int0^oox^(2n+1) e^ (-x^2)...

Prove that: `I_n=int_0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N`.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  2. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u)du ...

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  3. Prove that: In=int0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N.

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  4. Solve the following 2lt=|x-2|lt=5

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  5. The value of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  6. It is known that f(x) is an odd function in the interval [-p/2, p/2] ...

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  7. If int(-1)^4 f(x) dx =4 and int2^4[3-f(x)]dx=7 then the value of int(...

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  8. If int0^(pi/2)logsinthetad(theta)=k , then find the value of int0^(pi...

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  9. Evaluate: int0^(pi/2)sinxcosxdx

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  10. Let f(x) is continuous and positive for x in [a , b],g(x) is continuou...

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  11. Evaluate: int(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest i...

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  13. Evaluate: int0^(2pi)[sinx]dx ,where[dot] denotes the greatest inte...

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  14. STATEMENT 1 : The value of int0^1tan^(-1)((2x-1)/(1+x-x^2)) dx=0 STA...

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  15. Evaluate: int0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest int...

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  16. STATEMENT 1 : On the interval [(5pi)/4,(4pi)/3]dot the least value of ...

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  17. Evaluate: int0^(10pi)[tan^(-1)x]dx ,w h e r e[x] represents greatest ...

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  18. Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0AAx ...

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  19. Evaluate: int0^((5pi)/(12))[tanx]dx , where [dot] denotes the grea...

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