Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

12,137 questions

16,800 answers

1,421 comments

10,643 users

need help solving this calc question

+1 vote

 

Find the average value of f(x) in the interval [-1,3] when f'(x)=3x^2-6x and f(2)=0?

asked Jan 18, 2013 in CALCULUS by homeworkhelp Scholar

2 Answers

+1 vote

The avarage value of f(x) in the interval [-1,3]

When

image

f(2) = ?

image

Note:image   Here image

Given that interval [-1,3]

image

There fore

image

image

Formula: image

image

image

Formula: image

image

image

image

image

image

image

image

image

Find f(2) = ?

image

image

image

image

Formula: image

image

image

image

image

image

image

image

answered Jan 18, 2013 by richardson Scholar

The average value of f (x ) in the interval [-1, 3], faverage  = 2.

0 votes

f '(x ) = 3x2 - 6x

Take integration to each side.

ʃ f '(x ) = ʃ (3x2 - 6x ) dx

f (x ) = ʃ (3x2 - 6x ) dx

= ʃ (3x2) dx - ʃ (6x ) dx

= 3ʃ x2 dx - 6ʃx dx

= 3(x3/3)  - 6(x2/2) + C

= x3  - 3x2 + C -> (1)

Condition is f(2) = 0.

0 = (2)3  - 3(2)2 + C

0 = 8  - 3(4) + C

0 = 8  - 12 + C

0 = -4 + C

C = 4

Substitute c value in(1)

f (x ) = x3  - 3x2 + 4

The average value of the function f (x ) over the interval [a, b] is image.

image

image

image

image

image

image

image

image

image

image

image

Therefore the average value of f (x ) in the interval [-1, 3], faverage  = 2.

 

 

answered Jul 7, 2014 by joly Scholar

Related questions

asked Sep 5, 2014 in CALCULUS by anonymous
asked Nov 11, 2014 in CALCULUS by anonymous
asked Apr 21, 2014 in CALCULUS by anonymous
asked Apr 21, 2014 in CALCULUS by anonymous
asked Nov 5, 2014 in CALCULUS by anonymous
asked Oct 25, 2014 in CALCULUS by anonymous
...