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If An=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,...

If `A_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,B_n=int_0^(pi/2)((sinn x)/(sinx))^2 dx` for `n inN `, Then
(A) `A_(n+1)=A_n` (B) `B_(n+1)=B_n` (C) `A_(n+1)-A_n=B_(n+1)` (D) `B_(n+1)-B_n=A_(n+1)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  2. F ind the value of int0^1logx dxdot

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  3. If An=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,Bn=int0^(pi/2)((sinn x)/(sinx)...

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  4. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

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  5. The value of int0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

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  6. Evaluate: int(sin^(-1)x)/(1-x^2)^(3//2)dx

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  7. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

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  8. Evaluate: int1^oo (e^(x+1)+e^(3-x))^(-1)dx

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  9. If f(x)=int(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

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  10. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

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  11. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

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  12. Prove that 4 lt= int1^3 sqrt(3+x^2) dx lt= 4sqrt(3)

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  13. If I1=int0^(pi//2)(cos^2x)/(1+cos^2x)dx , I2=int0^(pi//2)(sin^2x)/(1+s...

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  14. Prove that int0^1sqrt((1+x)(1+x^3))\ dx cannot exceed sqrt((15)/8).

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  15. Let T >0 be a fixed real number. Suppose f is continuous function su...

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  16. Evaluate: int0^1 1/(sqrt(1-x^2))sin^(-1)(2xsqrt(1-x^2))dxdot

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  17. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation x...

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  18. Evaluate: int(-pi//2)^(pi//2) sqrt(cosx-cos^3x) dx

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  19. If f(2-x)=f(2+x) and f(4-x)=f(4+x) for all x and f(x) is a function fo...

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  20. int(-1)^2|x^3-x|dxdot

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