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- int0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) p...
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- int0^oo(dx)/([x+sqrt(x^2+1)]^3)is equal to (a)3/8 (b) 1/8 (c) -3/8 ...
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- The value of int1^e (1+x^2 In x)/(x+x^2 In x) dx is equal (a) In (1+...
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- The value of integral int0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be...
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- Ifint0^oo(x^2dx)/((x^2+a^2)(x^2+b^2)(x^2+c^2)) =pi/(2(a+b)(b+c)(c+a...
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- The value of the integral int0^1(dx)/(x^2+2xcosalpha+1) is equal to ...
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- The natural number nle5 for which In=int0^1 e^x(x-1)^n dx=16-6e is
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- Let f be a continuous function on [a ,b]dot Prove that there exists a ...
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- If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), th...
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- Evaluate: int0^(1)sin^(-1)((2x)/(1+x^2))dx
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- Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...
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- L e t \ f(n)=1+1/2+1/3+...+1/n. Then show that f(n)=int0^(pi/2)cot(the...
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- Let f(x) be a continuous function AAx in R , except at x=0, such that...
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- If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...
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- Determine a positive integer n such that int0^(pi/2)x^nsinx dx=3/4(pi^...
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- f,g,h are continuous in [0,a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5...
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- If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...
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- Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...
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- Evaluate: int3^10[log[x]]dx
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- If the function f : [0,8] to R is differentiable, then for 0 < alpha...
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