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If f(x) is of the form f(x) = `a + bx + cx^2`, show that `underset(0)overset(1)intf(x) dx = 1/6 [f(0)+4f(1/2)+f(1)]`

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Prove that : underset(0)overset(2a)intf(x) dx = underset(0)overset(2a)intf(2a-x)dx

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Evaluate: underset(-2)overset(2)int(f(x) dx where f(x) = {:{(2x-1,-2lexle1),(3x-2,1lexle2)

For each of the following paris of function f(x) and g(x), verify that: underset(0)overset(1)int[f(x)+g(x)]dx = underset(0)overset(1)intf(x)dx+underset(0)overset(1)intg(x)dx: f(x) = 1, g (x) = x^2

For each of the following functions f(x), verify that: underset(0)overset(0)intf(x) dx = underset(0)overset(1)intf(x) dx + underset(1)overset(2)intf(x) dx: f(x) = x^2+2

For each of the following functions f(x), verify that: underset(0)overset(0)intf(x) dx = underset(0)overset(1)intf(x) dx + underset(1)overset(2)intf(x) dx: f(x) = x+2

For each of the following functions f(x), verify that: underset(0)overset(0)intf(x) dx = underset(0)overset(1)intf(x) dx + underset(1)overset(2)intf(x) dx:f(x) = e^x

For each of the following paris of function f(x) and g(x), verify that: underset(0)overset(1)int[f(x)+g(x)]dx = underset(0)overset(1)intf(x)dx+underset(0)overset(1)intg(x)dx: f(x) = e^x,g(x) = 1

Prove that following: underset(1)overset(3)intf(x) dx when f(x) = |x-1|+|x-2|+|x-3|

Evaluate underset(-1)overset2int f(x)dx , where f(x)=|x+1|+|x|+|x-1|

MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate the following integrals. underset(0)overset(1)int(1)/(sqrt(...

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

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

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

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

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

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  7. For each of the following paris of function f(x) and g(x), verify that...

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  8. For each of the following paris of function f(x) and g(x), verify that...

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  9. Evaluate the following integrals by changing the limits of integration...

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  10. Evaluate the following integrals by changing the limits of integration...

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  11. Evaluate the following integrals by changing the limits of integration...

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  12. Evaluate the following integrals by changing the limits of integration...

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  13. Evaluate the following integrals by changing the limits of integration...

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  14. Evaluate the following integrals by changing the limits of integration...

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  15. Evaluate the following integrals by changing the limits of integration...

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  16. Evaluate the following integrals by changing the limits of integration...

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  17. Evaluate the following integrals by changing the limits of integration...

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  18. Evaluate the following integrals by changing the limits of integration...

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  19. Evaluate the following integrals by changing the limits of integration...

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  20. Evaluate the following integrals by changing the limits of integration...

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