I. FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: 1. The loop of y = x *(4 - x) 2. у %3 бх - х, y = x²– 2x 3. y = 2x y? + 4x - 8 = 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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I.
FIND THE AREA BOUNDED BY THE FF CURVES AND LINES:
1. The loop of y = x *(4 - x)
2. у 3 бх — х,
y = x²- 2x
3. у %3D2х
y? + 4x – 8 = 0
4. An arch of y =(1/3)sin(x/3)
5. 4y = x2 - 2lnx,
y = 0, x = 1, x = 4
6. y? - 6y = - x
Y? - 2y = x
1
7. y=:
1+x
y=0, x =1, x = - 1
8. of one loop of the curve r = cos? 0- sin? 0
9. y = 4/x, y- 4y + 2x = 5 and the line y = 4
10. 1* quadrant area of y = (4-x)/(x+2)?
II.
FIND THE VOLUME OF THE SOLID FORMED BY REVOLVING THE GIVEN AREA
BOUNDED BY THE LINES AND CURVES, ABOUT A GIVEN AXIS OF ROTATION.
1. y = 3cos(x/2) the y axis and the x axis in the 1* quadrant revolved about the x-axis.
2. The area bounded by y=3x+4 and the curve y=x is revolved about the line x =5.
3. The area bounded by the curve y = x, x= 0 and y = 1 is revolved about the x axis.
III.
EVALUATE THE F. ITERATED INTEGRALS
ea/2 ptan y secy
14 2sinx cycosx
1. ["T"
x'cos ydxdy
y dz dy dx
12
2. cosy sin2x dy dx
5. [LT" xydx dz dy
Jo
e/2pcos x pr-X
3 SI ye* dr dy
6. [ T* sin(x + y)dy dz dx
3.
Transcribed Image Text:I. FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: 1. The loop of y = x *(4 - x) 2. у 3 бх — х, y = x²- 2x 3. у %3D2х y? + 4x – 8 = 0 4. An arch of y =(1/3)sin(x/3) 5. 4y = x2 - 2lnx, y = 0, x = 1, x = 4 6. y? - 6y = - x Y? - 2y = x 1 7. y=: 1+x y=0, x =1, x = - 1 8. of one loop of the curve r = cos? 0- sin? 0 9. y = 4/x, y- 4y + 2x = 5 and the line y = 4 10. 1* quadrant area of y = (4-x)/(x+2)? II. FIND THE VOLUME OF THE SOLID FORMED BY REVOLVING THE GIVEN AREA BOUNDED BY THE LINES AND CURVES, ABOUT A GIVEN AXIS OF ROTATION. 1. y = 3cos(x/2) the y axis and the x axis in the 1* quadrant revolved about the x-axis. 2. The area bounded by y=3x+4 and the curve y=x is revolved about the line x =5. 3. The area bounded by the curve y = x, x= 0 and y = 1 is revolved about the x axis. III. EVALUATE THE F. ITERATED INTEGRALS ea/2 ptan y secy 14 2sinx cycosx 1. ["T" x'cos ydxdy y dz dy dx 12 2. cosy sin2x dy dx 5. [LT" xydx dz dy Jo e/2pcos x pr-X 3 SI ye* dr dy 6. [ T* sin(x + y)dy dz dx 3.
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