Integration - Quiz 1

Question 1

Which of the following is the indeﬁnite integral of $x2 + 7 ?$

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

Which of the following is the indeﬁnite integral of $x 13 ?$

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

Which of the following is the indeﬁnite integral of $2-? x2$

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

Which of the following correctly evaluates the deﬁnite integral $∫ 3 2 (x + 3x+ 2)dx ? 1$

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

Which of the following correctly evaluates the deﬁnite integral $∫ 2 -2 -3 -1(x + 3x + 2)dx?$

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.


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