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Each question contains statements given in two columns which have to be matched. Statements (a,b,c,d) in column I have to be matched with statements (p,q,r,s) in column II. If the correct match are a-p, s, b-r c-p, q. and d-s, then the correctly bubbled `4x4` matrix should be as follows: figure Column I, a) If `int(2^x)/(sqrt(1-4^x))dx=ksin^(-1)(f(x))+C ,` then `k`is greater than, b) If `int((sqrt(x))^5)/((sqrt(x))^7+x^6)dx=aln(x^k)/(x^k+1)+c ,` then `a k`is less than, c) If `int(x^4+1)/(x(x^2+1)^2)dx=kln|x|+m/(1+x^2)+n ,` where `n`is the constant of integration, then `m k`is greater than, d) If `int(dx)/(5+4cosx)=ktan^(-1)(mt a n x/2)+C ,` then `k//m`is greater than, COLUMN II p) 0 q) 1 r) 3 s)4

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  2. Let f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot The...

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

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

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

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

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

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

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

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

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

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

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

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  18. int(secx)/(sqrt(cos2x))dx is equal to

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  19. Evaluate : int(x^2+20)/((xsinx+5cosx)^2)dx

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  20. int(x+2)/((x^2+3x+3)(sqrt(x+1))).dx

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