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If n is an odd natural number, then in...

If n is an odd natural number, then
`int_(-pi//6)^(pi//6) (pi+4x^(n))/(-sin(pq+(pi)/(6))dx=`

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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of the definite integral int(0)^(1)(1+e^(-x^(2))) dx is

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  2. If I=int(-pi)^(pi) (sin^(2))/(1+a^(x))dx, a gt 0, then I equals

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  3. If n is an odd natural number, then int(-pi//6)^(pi//6) (pi+4x^(n))/...

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  4. If I(1)=int(0)^(x) e^("zx "e^(-z^(2)))dz and I(2)=int(0)^(x) e^(-z^(2)...

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  5. int(0)^(1//2) |sin pi s|dx is equal to

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  6. The function F(x)=int(0)^(x) log((1-x)/(1+x))dx, is

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  7. int(1//3)^(3) (1)/(x)sin ((1)/(x)-x)dx is equal to

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  8. If F(x)=int(x^(2))^(x^(3)) log t dt (x gt 0), then F'(x) equals

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  9. If F(x)and g(x) are two integralable functions defined on [a,b], the...

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  10. If I=int(0)^(1) (dx)/(sqrt(1+x^(4)))dx then

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  11. If I=int(0)^(1) (dx)/(1+x^(4)), then

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  12. The value of int(-1)^(1) x|x|dx, is

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  13. If int(0)^(pi//2) cos^(n)x sin^(n) x dx=lambda int(0)^(pi//2) sin^(n)x...

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  14. The value of int(1//e )^(e )(|log x|)/(x^(2))dx, is

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  15. Assuming that f is everywhere continuous, (1)/(c )int(ac)^(bc)f((x)/(c...

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  16. (d)/(dx)(int(f(x))^(g(x)) phi(t)dt) is equal to

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  17. If f(x)=ae^(2x)+be^(x)+c x satisfies the conditions f(0)=-1, f'(log 2)...

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  18. The value of int(0)^(2) |cos((pix)/(2))| is

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  19. If int(0)^(1) cot^(-1)(1-x-x^(2))dx=k int(0)^(1) tan^(-1)x dx, then k=

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  20. If 0 lt a lt 1, then int(-1)^(1) (1)/(sqrt(1-2ax+a^(2)))dx is equal to

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