Math 207 Review of Integral Calculus by ijk77032

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									Math 207                                                             Review of Integral Calculus
1. Explain what a definite integral is and what it represents geometrically.
2. State the Fundamental Theorem of Calculus and outline a proof.
3. Find each of the following derivatives:
      d   4 2
a.      ( ex dx)
     dx 0

      d   x t2
b.   dx ( 3 e dt)

      d   4 t2
c.   dx ( x e dt)

      d   x3     2
d.   dx ( 0    et dt)
      d   g(x)
e.      (
     dx f (x)
                 h(t)dt)

4. Evaluate the following definite/indefinite integrals. Do not use a calculator.
          1 x                                       1   1
a.        0 4−x2
                     dx                      b.     0 4−x2
                                                                    dx


          1   1                                    ∞            2
c.        0 4+x2
                     dx                      d.    0
                                                         xe−x       dx


          ∞                                        1
e.            xe−x dx                        f.      √ 1            dx
          0                                        0  1−x2


       1                                          1          √
g.       √ 1         dx                      h.     (x   + 1) x dx
       0  1+x2                                    0


      1    √                                       1   x
i.    0
          x x + 1 dx                         j.    −1 1+x8
                                                                    dx


          cos 3x                                   ∞ x
k.     (1+4 sin 3x)2    dx                   l.    0 1+x4
                                                                    dx

          π
m.        2
          0
              cos3 x dx                      n.     arctan x dx




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