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"Let " k(x)=int((x^(2)+1)dx)/(root(3)(x^...

`"Let " k(x)=int((x^(2)+1)dx)/(root(3)(x^(3)+3x+6)) " and " k(-1)=(1)/(root(3)(2)). " Then the value of " k(-2) " is "-.`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a)1/2(ln((x-1)/(x+1)...

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  2. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

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  3. "Let " k(x)=int((x^(2)+1)dx)/(root(3)(x^(3)+3x+6)) " and " k(-1)=(1)/(...

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  4. Column I a) int(x^2-x+1)/(x^3-4x^2+4x)dx b) int(x^2-1)/(x(x-2)^3)dx ...

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  5. Let f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot The...

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  6. Each question contains statements given in two columns which have to b...

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  7. The value of ∫e^2x ( 1/x ​ − 1/(2x^2) ​ )dx is

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  8. Statement 1: If the primitive of f(x)=pisinpix+2x-4 has the value -2 f...

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  9. Let f(x)=2^(2x−1)and ϕ(x) =−2^x+2xlog2. If f'(x)>ϕ'(x), then value of ...

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  10. Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-...

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  11. If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b...

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  12. If f(x)=int(3x^2+1)/((x^2-1)^3)dx and f(0)=0, then the value of |2/(f(...

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  13. Evaluate: intsqrt((1-sqrt(x))/(1+sqrt(x)))dx

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  14. "If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...

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  15. The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...

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  16. Let f(x)=int(x^2dx)/((1+x^2)(1+sqrt(x^2+1)))a n df(0)=0. Then value o...

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  17. If y=intsqrt(x)(1+x^(1/3))^4dx is equal to

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  18. If intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l co...

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  19. Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is

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  20. Evaluate: int(sin2x)/(sin^4x+cos^4x)dx

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