Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

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

13,435 questions

17,804 answers

1,438 comments

774,866 users

areas and distances

0 votes
. Estimate the area under the graph of f(x) = (1/ 1+4x^2) from x = −2 to x = 0 using four approximating rectangles and

(a) right endpoints (R4).

(b) left endpoints (L4).

(c) midpoints (M4). Carry any intermediate calculations to four decimal places, and round your final results to two decimal place
asked Apr 11, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(a)

Step 1:

The function is  on interval is .

Number of rectangles are .

The sum of all circumscribed rectangle is upper sum.

, where .

Where .

Find the upper sum.

The right end point is .

Area of upper sum is .

image

Area of upper sum is image sq-units.

Solution:

Area of upper sum is image sq-units.

answered Apr 11, 2015 by Sammi Mentor
edited Apr 11, 2015 by Sammi

Contd...

Check the solution by using the graph.

image

0 votes

(b)

Step 1:

The function is  on interval is .

Number of rectangles are .

The sum of all inscribed rectangle is upper sum.

, where .

Width  .

Find the lower sum.

The left end point is .

image.

Area of lower sum is image.

image

Area of lower sum is image sq-units.

Solution:

Area of lower sum is image sq-units.

answered Apr 11, 2015 by Sammi Mentor
edited Apr 11, 2015 by Sammi

Contd...

Check the solution by using the graph.

image

0 votes

(c)

Step 1:

The function is  on interval is .

Number of rectangles are .

Using Midpoint Rule:

The area is .

Consider .

.

Substitute in .

.

Substitute image values.

and .

.

Step 2:

Using Midpoint Rule:

Area =

Area of the region by using Midpoint Rule is image sq-units.

Solution:

image sq-units.

answered Apr 11, 2015 by Sammi Mentor
edited Apr 11, 2015 by Sammi

Contd...

Check the solution by using the graph.

image.

...