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.

13,428 questions

17,804 answers

1,438 comments

47,198 users

Area Between Two Curves:?

+2 votes
Find the area of the shaded region bounded by y = 7 x and y = x (sqrt{(15^{2}-x^{2})}. )

A=
asked Feb 9, 2013 in CALCULUS by skylar Apprentice

1 Answer

+2 votes

y = 7x and y = x√(152 - x2)

7x - x√(152 - x2) = 0

x[7 - √(152 - x2)] = 0

.x = 0 or [7 - √(152 - x2)] = 0

Take [7 - √(152 - x2)] = 0

Subtract -7 from each side and multiply each side by negative one.

√(152 - x2) = 7

Take square each side.

225 - x2 = 49 ⇒ x2 = 225-49=176⇒x =√176 ⇒ x = ±13.26

The two equation interval is (13.26, 0, -13.26)

In interval 0<x<13.26, y>y which makes enclosed area A₁.

In interval -13.26<x<0,y>y which makes enclosed area A₂.

The area between two curves is A₁= ʃ(y₂-y₁)dx

y₂ - y₁ = image

image

image

Integrals with roots image

image

image

image

image

image

image

image

image

y₁ - y₂ = image

image

image

image

image

image

image

image

image

image

Total area is A = A₁ + A₂ = 394.666+394.666 = 789.332 unit2.

answered Feb 12, 2013 by britally Apprentice

Related questions

asked Nov 11, 2014 in PRECALCULUS by anonymous
asked Dec 5, 2014 in CALCULUS by anonymous
...