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int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(...

`int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx` i s equal to `(pi^2)/6` (b) `(pi^2)/3` (c) `(pi^2)/8` (d) `(3pi^2)/8`

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int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx is equal to (pi^2)/6 (b) (pi^2)/3 (c) (pi^2)/8 (d) (3pi^2)/8

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CENGAGE ENGLISH-INTEGRALS-All Questions
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  2. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

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  3. int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to...

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  4. Ifint(-pi/4)^((3pi)/4)(e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx))=kint(-p...

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  5. If f(x) =(e^x)/(1+e^x), I1=int(f(-a))^(f(a)) xg(x(1-x))dx, and I2=int(...

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  6. If f(y)=e^y ,g(y) = y>0,a n d \ F(t)=int0^t f(t-y)g(y)dy ,then

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  7. G i v e nint0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integr...

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  11. 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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  12. The value of integral int0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be...

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  13. 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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  14. The value of the integral int0^1(dx)/(x^2+2xcosalpha+1) is equal to ...

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  15. Determine a positive integer nlt=5 such that int0^1e^x(x-1)^n=16-6e

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  16. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

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  17. 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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  18. Evaluate: int0^(1)sin^(-1)((2x)/(1+x^2))dx

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  19. Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...

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  20. 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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