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Prove that int(0)^(oo) (sin^(2)x)/(x^(2)...

Prove that `int_(0)^(oo) (sin^(2)x)/(x^(2))dx=int_(0)^(oo) (sinx)x dx`

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To prove that \[ \int_{0}^{\infty} \frac{\sin^2 x}{x^2} \, dx = \int_{0}^{\infty} \frac{\sin x}{x} \, dx, \] we will follow these steps: ...
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CENGAGE ENGLISH-DEFINITE INTEGRATION -SOLVED EXAMPLE_TYPE
  1. f,g, h , are continuous in [0, a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-...

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  2. Evaluate int(0)^((pi)/2)(sin3x)/(sinx+cosx) dx.

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  3. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  4. Prove that int(0)^(oo) (sin^(2)x)/(x^(2))dx=int(0)^(oo) (sinx)x dx

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  5. If int0^(pi/2)logsinthetadtheta=k , then find the value of int0^(pi/2)...

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  6. Evaluate : int0^pi(x^2sin2x*sin(pi/2*cosx))/(2x-pi)dx

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  7. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

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  8. It is known that f(x) is an odd function and has a period p. Prove tha...

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  9. Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...

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  10. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

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  11. Let f(x) be a continuous function AAx in R , except at x=0, such that...

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  12. If xint0^xsin(f(t))dt=(x+2)int0^x tsin(f(t))dt ,w h e r ex >0, then sh...

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  13. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

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  14. Let a+b=4,w h e r ea<2,a n dl e tg(x) be a differentiable function. If...

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  15. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

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  16. If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...

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  17. Suppose f is a real-valued differentiable function defined on [1,oo] w...

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  18. Let f be a continuous function on [a , b]dot If F(x)=(inta^xf(t)dt-int...

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  19. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

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  20. If f(x)=x+int0^1 t(x+t) f(t)dt, then find the value of the definite in...

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