Integration - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following is the indefinite integral of   x2 + 7 ?
a) ∫
  (x2 + 7)dx = 2x + c.    b) ∫
  (x2 + 7)dx = x3 + 7x.
c) ∫
 (x2 +7)dx = 1x3 + 7x.
             2    d) ∫             1
  (x2 + 7)dx = -x3 + 7x+ c .
              3

 

Not correct. Choice (a) is false.
Try again, you seem to be mixing up integration and differentiation.
Not correct. Choice (b) is false.
Try again, recall ∫
  xndx = --1--xn+1,
         n + 1  and you should add a constant of integration.
Not correct. Choice (c) is false.
Try again, recall ∫          1
  xn dx = ----xn+1 .
          n+ 1
Your answer is correct.
Since ∫           1
   xndx = -----xn+1
          n +1  integrating term by term we have ∫             1
  (x2 + 7)dx = -x3 + 7x+ c ,
              3  noting that we add a constant of integration.
Question 2 lion

Which of the following is the indefinite integral of   x 13 ?
a) ∫
  x 13 dx = 4x43 + c.
          3    b) ∫
  x13 dx = 3 x23 + c.
         2
c) ∫
  x 13 dx = 1x- 23 + c.
          3    d) ∫
  x13 dx = 3x43 + c.
          4

 

Not correct. Choice (a) is false.
Try again, recall that 1-= 3 .
43   4
Not correct. Choice (b) is false.
Try again, recall that 1 + 1 = 4.
3       3
Not correct. Choice (c) is false.
Try again, you seem to have differentiated   2x 12 .
Your answer is correct.
Since 1+ 1 = 4
3      3  we have ∫
   x13 dx = 3x 43 + c.
          4
Question 3 lion

Which of the following is the indefinite integral of   2-?
x2
a) ∫
   2-dx = - 2+ c.
   x2       x    b) ∫
  -2 dx = 2+ c.
  x2      x
c) ∫
  -2 dx = --6 + c.
  x2       x3    d) ∫
   2-dx = -6 + c.
   x2     x3

 

Your answer is correct.
∫         ∫
   2-dx =   2x-2dx = - 2x -1 + c = - 2-+ c.
   x2                             x
Not correct. Choice (b) is false.
Try again looking carefully at the sign.
Not correct. Choice (c) is false.
Try again, you have differentiated.
Not correct. Choice (d) is false.
Try again, you have almost differentiated, watch the sign of the index.
Question 4 lion

Which of the following correctly evaluates the definite integral ∫ 3  2
   (x + 3x+ 2)dx ?
 1
a) 97
-3 .    b) 110
 3 .
c) 74
 3 .    d) 4.

 

Not correct. Choice (a) is false.
Try again, you seem to have added the two components of the definite integral instead of subtracting them.
Not correct. Choice (b) is false.
Try again, you appear not to have integrated correctly. Note that ∫                  [              ]
  3  2              1  3  3 2      3
 1 (x + 3x + 2) dx = 3 x + 2x  +2x  1 .
Your answer is correct.
∫ 3
   (x2 + 3x+ 2)dx
 1  =[1     3      ]3
 3x3 + 2x2 + 2x
               1
 =    27       1   3
[9 + 2-+ 6]- [3 + 2 + 2]
 =57 - 23=  74.
 2   6    3
Not correct. Choice (d) is false.
Try again, you appear not to have integrated correctly. Note that ∫ 3                [             ]3
   (x2 + 3x+ 2)dx = 1x3 + 3x2 + 2x  .
 1                  3     2       1
Question 5 lion

Which of the following correctly evaluates the definite integral ∫
  2  -2     -3
 -1(x   + 3x  + 2)dx?
a) ∫
  2  - 2    -3
  -1(x   + 3x  + 2)dx = - 3 .    b) ∫ 2  -2     -3          5
   (x   +3x   + 2)dx = 58 .
 -1
c) ∫
  2  -2    -3
 -1(x  + 3x   + 2)dx = - 5.    d) ∫ 2  -2    -3           3
   (x  + 3x   +2)dx = 616 .
 -1

 

Not correct. Choice (a) is false.
Try again, you may have made a mistake with a sign.
Your answer is correct.
∫ 2
   (x-2 + 3x-3 + 2)dx
 -1  =[              ]2
 - 1-- -32 +2x
   x   2x       -1
 =[- 1- 3 + 4]- [1 - 3- 2]
   2  8           2
 =25     20   45    5
8-- (- 8-) =-8 = 58 .
Not correct. Choice (c) is false.
Try again, you may have made a mistake with a sign.
Not correct. Choice (d) is false.
Try again, you may have differentiated instead of integrated.