Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.) fx) 3 9 — х2, [-3, 3] y 10- 6. 4 X -2 Give the exact area obtained using a definite integral. 2.

Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.) fx) 3 9 — х2, [-3, 3] y 10- 6. 4 X -2 Give the exact area obtained using a definite integral. 2.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...

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Question

Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.)
fx) 3 9 — х2, [-3, 3]
y
10-
6.
4
X
-2
Give the exact area obtained using a definite integral.
2.

Expert Solution

Step 1

Given that $f (x) = 9 - x^{2}, [- 3, 3]$

We have to find the approximate area by the rectangle given as yellow

Then find exact area by definite integral.

Step 2

Find the approximate area:

Here A, B, C, D are the rectangles

C and D are congruent to B and A respectively

Length of A is $4$ and breadth of A is $1.5$

Length of B is $8.5$ and breadth of B is $1.5$

Area of A $= l \times b = 4 \times 1.5 = 6$

Area of B $= l \times b = 8.5 \times 1.5 = 12.75$

Area of C $=$ Area of B $= 12.75$

Area of D $=$ Area of A $= 6$

Area of the whole rectangle area $= 6 + 12.75 + 12.75 + 6 = 37.5$ sq. units.

Approximate area of the given curve is $37.5$ sq.units.

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