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Show that int0^(pi/2)sqrt((sin2theta))si...

Show that `int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4`

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: int(-pi)^pi(xsinx dx)/(e^x+1)

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  2. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,then lambda is e...

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  3. Show that int0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

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  4. The number of positive continuous f(x) defined in [0,1] for with I(1)=...

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  5. int 0^(pi/2) (sin^2x)/(sinx+cosx)dx

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

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  7. For theta in (0,pi/2), prove that int0^theta"log"(1+tanthetatanx)dx=th...

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  8. A function f is defined by f(x)=1/(2^(r-1)),1/(2^r)ltxlt=1 (2^(r-1)),...

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  9. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

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  10. If P(x) is a polynomial of the least degree that has a maximum equal t...

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  11. Evaluate: int0^pixlogsinxdx

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  12. The value of the definite integral int0^(sqrt(1n(pi/2)))cose^(x^(2)...

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  13. Evaluate: int0^(π/2)cos2x+4sin2x cos2xdx

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  14. T h ev a l u eofint1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dxi...

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  15. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

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  16. If f(x) is monotonic differentiable function on [a , b] , then int...

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  17. Find the value of : int0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denote...

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

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  19. L e tA=int0^oo(logx)/(1+x^3)dx Then find the value of int0^oo(xlogx)/(...

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  20. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R , w...

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