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Prove that following: underset(0)overset...

Prove that following: `underset(0)overset(1)inttan^-1 x dx = pi/4 - 1/2 log 2`

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate the following: underset(0)overset(k)int(dx)/(2+8x^2)= pi/16, ...

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  2. Prove that following: underset(0)overset(1)int xe^x dx = 1

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  3. Prove that following: underset(0)overset(1)inttan^-1 x dx = pi/4 - 1/2...

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  4. Prove that following: underset(0)overset(a)int3x^2dx=8, find the value...

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  5. Evaluate the following integrals. underset(0)overset(pi//4)inttan^4 ...

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  6. Evaluate the following integrals. underset(0)overset(pi//2)intx^2 si...

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  7. Evaluate the following integrals. underset(0)overset(pi//2)int cos 2...

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  8. Evaluate the following integrals. underset(-1)overset(1)int(x+1)/(x^...

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  9. Evaluate the following integrals. underset(1)overset(2)int(dx)/((x-1...

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  10. Evaluate the following integrals. underset(1)overset(3)int(x+3)/(x(x...

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  11. Evaluate the following integrals. underset(1)overset(3)int(dx)/(x^2(...

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  12. Evaluate the following integrals. underset(0)overset(pi)int(xdx)/(a^...

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  13. Evaluate the following integrals. underset(3)overset(4)int(2x)/(sqrt...

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  14. Evaluate the following integrals. underset(pi//2)overset(pi)inte^x(1...

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  15. Evaluate the following integrals. underset(1)overset(2)int(1/x-1/(2x...

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  16. Evaluate the following integrals. underset(0)overset(1)int(1)/(sqrt(...

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  17. Prove that underset(0)overset(pi//2)int cos^4 x dx = (3pi)/16

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  18. If f(x) is of the form f(x) = a + bx + cx^2, show that underset(0)over...

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  19. For each of the following functions f(x), verify that: underset(0)over...

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  20. For each of the following functions f(x), verify that: underset(0)over...

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