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If In=int0^(pi//4)tan^("n")x dx , prov...

If `I_n=int_0^(pi//4)tan^("n")x dx` , prove that `I_n+I_(n-2)=1/(n-1)dot`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate the following integrals: int0^1(24x^3)/((1+x^2)^4)dx

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  2. Evaluate the following integrals: int0^1sqrt((1-x)/(1+x))dx

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  3. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n-1)dot

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  4. If In=int0^(pi//4)tan^n x dx , show that 1/(I2+I4),1/(I3+I5),1/(I4+...

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

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  6. Find dy/dx if x^2=cosy

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  7. Evaluate: int0^a1/((x^2+a^2))dx (ii) int0^oo(x^2)/((a^2+x^2)^(5//2))dx

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  8. Evaluate: int0^1xsqrt((1-x^2)/(1+x^2))dx

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  9. Evaluate the following integrals: int (sin)^(-1)sqrt(x/(a+x))dx

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  10. Evaluate the following integrals: int1^2 1/(x(1+logx)^2)dx

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  11. Evaluate the following integrals: int0^(pi//4)(sin^2xcos^2x)/((sin...

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  12. Evaluate the following integrals: int0^(pi//2)(tanx)/(1+m^2tan^2x)d...

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  13. Evaluate: int0^1|5x-3|dx (ii) int0^pi|cosx|dx (iii) int(-5)^5|x-2...

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  14. Evaluate: (i) \int(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=...

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  15. int (1)^x 1/x dx =

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  16. If a >0, find int0^(3a)|x^2-a^2|dxdot

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  17. If [dot] denotes the greatest integer function, then find the valu...

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  18. Evaluate: int0^3[x]dx

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  19. int0^1d/(dx){sin^(-1)((2x)/(1+x^2))}dx is equal to 0 (b) pi (c) ...

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  20. Evaluate the following integrals: int(-a)^a(xe^x^2)/(1+x^2)dx

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