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Prove that: int0^(2pi)(xsin^(2n)x)/(si...

Prove that: `int_0^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx`= `pi^2`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

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  2. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

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  3. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= pi^2

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  4. Prove that 1 lt underset(0)overset(2)int((5-x)/(9-x^(2)))dx lt 6/5

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  5. If the difference between the roots of the equation x^2+""a x""+""1...

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  6. If m is the least value (global minimum) and M is the greatest value (...

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  7. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  8. Show that inta^b(|x|)/x dx=|b|-|a|dot

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  9. The value of (pi^2)/(1n3)int(7/6)^(5/6)sec(pix)dxi s

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  10. Let: f(x)=int0^x|2t-3|dtdot Then discuss continuity and differentiabil...

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  11. If inta^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is

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  12. L e tI1=int(pi/6)^(pi/3)(sinx)/x dx ,I2=int(pi/6)^(pi/3)sin(sinx)/(sin...

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  13. The value of int0^1e^(x^2-x)dx is (a)<1 (b) >1 (c) > e^(-1/4) ...

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  14. Evaluate: int0^(1)x(dx)/(sqrt(1-x^(2)))

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  15. The value of the definite integral int(0)^(1)(1+e^(-x^(2))) dx is

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  16. Prove that 0 lt int0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8

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  17. Let a , b , c be nonzero real numbers such that int0^1(1+cos^8x)(a x^2...

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  18. Evaluate: 5050(int0^1(1-x^(50))^(100)dx)/(int0^1(1-x^(50))^(101)dx)

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  19. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,then evaluate (dy)/(d...

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  20. If f(x)=int0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a)f(x)+f...

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