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If int0^asqrt(x)dx=2aint0^(pi//2)sin^...

If `int_0^asqrt(x)dx=2aint_0^(pi//2)sin^3xdx` find the value of integral `int_a^(a+1)xdxdot`

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RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Mark the correct alternative in each of the following: int0^1sqrt(x...

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  2. Evaluate : int0^pi1/(1+sinx)dx

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  3. If int0^asqrt(x)dx=2aint0^(pi//2)sin^3xdx find the value of inte...

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  4. Evaluate: (i)int0^4 1/(sqrt(x^2+2x+3))dx (ii) int0^a1/(sqrt(a x-x...

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  5. If int0^1(3x^2+2x+k)dx=0, find the value of kdot

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  6. If int1^a (3x^2 + 2x +1)dx = 11 then the value of a is

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  7. If inta^b x^3dx=0, and If inta^b x^2dx=2/3, find a and b.

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  8. Evaluate: int0^(pi//2)sqrt(1-cos2x)dxdot

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  9. Evaluate: int0^(pi//2)sin^4xdx

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  10. Evaluate: int0^(pi//4)sqrt(1+sin2x)dx (ii) int0^(pi//4)sqrt(1-sin2x...

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  11. Evaluate: int(pi//4)^(pi//2)sqrt(1-sin2x)dx

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  12. Evaluate the following integrals: (1-35) int(-2)^2(3x^3+2|x|+1)/(x^...

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  13. Evaluate the following integrals: (1-35) int0^pixsinx cos^2x dx

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

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  15. For x >0,l e tf(x)=int1^x((log)e t)/(1+t)dtdot Find the function...

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  16. Evaluate the following integrals: (1-35) int0^(pi//2)(sin^n x)/(sin...

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

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  18. Prove that: int0^(pi//2)log|tanx+cotx|dx=pi(log)e2

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  19. Evaluate: int(-2)^2|xcospix|dx

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  20. Evaluate: int(-pi//2)^(pi//2)log(sinx+cosx)dx

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