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3a int(0)^(1) ((ax-1)/(a-1))^(2) dx is...

`3a int_(0)^(1) ((ax-1)/(a-1))^(2) dx` is equal to

A

`a-1+(a-1)^(-2)`

B

`a+a^(-2)`

C

`a-a^(-2)`

D

`a^(2)+1/(a^(2))`

Text Solution

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The correct Answer is:
A
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
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  2. int(0)^(1) (dx)/(e^(x) +e^(-x)) dx is equal to

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  3. 3a int(0)^(1) ((ax-1)/(a-1))^(2) dx is equal to

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  4. int (0) ^(pi//4) sin (x- [x])d (x-[x]) is equal to

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  5. The function L(x)=int(1)^(x)(dt)/t satisfies the equation

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  6. If overset(b)underset(a)int {f(x)-3x}dx=a^(2)-b^(2), then the value of...

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  7. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

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  8. int(0)^(pi//4)(cosx-sinx)dx+int(pi//4)^(5pi//4)(sinx-cosx)dx+int(2pi)^...

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  9. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^s in x^3dx=F(k)-...

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  10. Suppose that F (x) is an antiderivative of f (x)=sinx/x,x>0 , then...

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  11. The value of integral int (1//pi)^(2//pi)(sin(1/x))/(x^(2))dx=

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  12. The value of the integral int(0)^((pi)/4)(sqrt(tanx))/(sinx cos x) dx ...

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  13. If I(n) = int (0)^(pi//4) tan^(n) theta " " d theta, "then "I(8)+I(6)=

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  14. If g(1)=g(2), then int(1)^(2)[f{g(x)}]^(-1)f'{g(x)}g'(x)dx is equal to

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  15. If int(0)^(k)(dx)/(2+18x^(2))=(pi)/(24), then the value of k is

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  16. int(-1)^(0) (dx)/(x^(2) + 2x + 2 ) is equal to

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  17. The value of int(0)^(1)(x^(2))/(1+x^(2))dx is

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  18. The value of int0^1 (x^4+1)/(x^2+1)dx is

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  19. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  20. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

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