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Prove that: int0^(2a)f(x)dx=int0^(2a)...

Prove that: `int_0^(2a)f(x)dx=int_0^(2a)f(2a-x)dxdot`

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Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

Prove that int_-2^2 f(x^4)dx=2int_0^2 f(x^4)dx

If f is an integrable function such that f(2a-x)=f(x), then prove that int_0^(2a)f(x)dx=2int_0^af(x)dx

Statement-1: int_(0)^(pi//2) (1)/(1+tan^(3)x)dx=(pi)/(4) Statement-2: int_(0)^(a) f(x)dx=int_(0)^(a) f(a+x)dx

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate: int0^(pi/2) (sin^2x)/(1+sinxcosx) dx

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  2. Prove that: int0^(pi//2)(sin x)/(sinx-cosx)dx=pi/4

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  3. Prove that: int0^(2a)f(x)dx=int0^(2a)f(2a-x)dxdot

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  4. Evaluate: int(-pi//4)^(pi//4)x^3sin^4xdx (ii) int( a)^asqrt((a-x)...

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  5. Evaluate: int(pi//4)^(pi//4)(x+pi//4)/(2-cos2x)dx

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  6. Evaluate:int0^(pi//2)(cosx)/(1+cosx+sinx)dx

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  7. Prove that: int0^pix/(1-cosalphasinx)dx=(pi(pi-alpha))/(sinalpha)

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  8. Evaluate the following integrals: (1-35) int(-a)^a log((a-sintheta...

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  9. Evaluate the following integrals: int(-1)^1|xcospix|dx

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  10. Evaluate the following integrals: (1-35) int0^pi(x/(1+sin^2x)+cos^7...

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  11. Evaluate : int0^pix/(1+sinalphasinx)dx

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  12. Evaluate the following integrals: (1-35) int0^(pi//2)(asinx+bcosx)/...

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  13. Evaluate the following integrals as limit of sums: int0^2(x+4)dx (...

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  14. Evaluate int1^4(x^2-\ x)\ dx as a limit of sums.

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  15. Evaluate: inta^bsinx dx using limit of sum

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  16. Mark the correct alternative in each of the following: int0^1sqrt(x...

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

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

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

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

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