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Evaluate the following : int(4)^(7)((...

Evaluate the following :
`int_(4)^(7)((11-x)^(3))/(x^(3)+(11-x)^(3))dx`

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AI Generated Solution

To evaluate the integral \[ I = \int_{4}^{7} \frac{(11-x)^{3}}{x^{3} + (11-x)^{3}} \, dx, \] we can use a property of definite integrals. Specifically, we can exploit the symmetry of the integral by substituting \( x \) with \( 11 - x \). ...
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-DEFINITE INTEGRALS-Examples for Practice
  1. Evaluate the following : int(0)^(1)(dx)/(x+sqrt(1-x^(2))).

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  2. Evaluate the following : int(0)^(a)(sqrtx)/(sqrtx+sqrt(a-x))dx

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  3. Evaluate the following : int(0)^(a)(rootn(x+c))/(rootn(x+c)+rootn(a...

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  4. Evaluate the following : int(0)^(a)x^(2)sqrt(1-x)dx

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  5. Evaluate the following : int(0)^(1)x^(2)(1-x)^((5)/(2))dx.

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  6. Evaluate the following integral: int0^oo(logx)/(1+x^2)dx

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  7. Evaluate the following : int(0)^(pi//2)sin 2x.log (tanx)dx.

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  8. Evaluate the following : int(0)^(pi)(x tan x)/(secx+cos x)dx

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  9. Evaluate the following : int(0)^(pi)(x tanx)/(secx "cosec x")dx

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  10. Evaluate the following : int(0)^(pi)x sin^(3)x dx

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  11. Evaluate int(0)^(pi)(x)/((a^(2)cos^(2)x+b^(2)sin^(2)x))dx.

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  12. Evaluate the following : int(pi//6)^(pi//3)(root3(sinx))/(root3(sin...

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  13. Evaluate the following : int(pi//6)^(pi//3)(1)/(1+sqrt(cotx))dx

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  14. Evaluate the following : int(4)^(7)((11-x)^(3))/(x^(3)+(11-x)^(3))d...

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  15. Evaluate the following : int(1)^(3)(root3(x+5))/(root3(x+5)+root3(9...

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  16. int0 ^(pi/2) log sinx dx = int0 ^(pi/2) log cosx dx = 1/2 (pi) log(1/2...

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  17. int0^1 (log x)/(sqrt(1-x^2))dx

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  18. Evaluate the following : int(-9)^(9)(x^(3))/(4-x^(2))dx

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  19. Evaluate the following : int(-1)^(1)(x^(2))/(1+x^(2))dx

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  20. int(-pi)^(pi) (2x(1+ sinx))/(1+ cos^(2))dx is

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