07 - Area Between Curves

Kuta Software - Infinite Calculus

Area Between Curves

Name___________________________________ Date________________ Period____

For each problem, find the area of the region enclosed by the curves.

1) y = 2x2 - 8x + 10 x2

y = - 2x - 1 2

x = 1 x = 3

y 8

2) x = 2 y2 + 12 y + 19 y2

x = - - 4 y - 10 2

y = -3 y = -2

y 8

6

6

4

4

2

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

x2

1

3) y = - 3x -

2

2

y = 3

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

4)

x3 y = -

+ 2x2

2

y = -x2 + 4x

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

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Worksheet by Kuta Software LLC

For each problem, find the area of the region enclosed by the curves. You may use the provided graph to sketch the curves and shade the enclosed region.

5) y = -2x2 - 1 y = -x + 3 x = 0 x = 1

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6

2 4 6 8x

6) y = 2 3 x2 y = x

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

-8

7) y = -x3 + 6x y = -x2

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

8) y = -2 sec2 x y = 2cos x x = 0 x = 4

y 4

3

2

1

-

-

2 -1

2

-2

-3

-4

x

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Area Between Curves

Name___________________________________ Date________________ Period____

For each problem, find the area of the region enclosed by the curves.

1) y = 2x2 - 8x + 10 x2

y = - 2x - 1 2

x = 1 x = 3

y 8

2) x = 2 y2 + 12 y + 19 y2

x = - - 4 y - 10 2

y = -3 y = -2

y 8

6

6

4

4

2

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

( ( )) 3 2x2 - 8x + 10 -

x2

- 2x - 1

dx

2

1

= 11

-8 -6 -4 -2 -2

2 4 6 8x

-4

-6

-8

( ( )) -2 2 y2 + 12 y + 19 -

y2 -

- 4 y - 10

dy

2

-3

29 = 4.833

6

x2

1

3) y = - 3x -

2

2

y = 3

y 8

6

4

2

4)

x3 y = -

+ 2x2

2

y = -x2 + 4x

y 8

6

4

2

-8 -6 -4 -2 -2

2 4 6 8x

-4

-6

-8

( ( )) 7

x2

1

3 - - 3x - dx

2

2

-1

128 = 42.667

3

-8 -6 -4 -2 -2

2 4 6 8x

-4

-6

-8

( ( )) 2 -x2 + 4x -

x3 -

+ 2x2

dx +

2

0

( ) 4 x3 -

+ 2x2 - (-x2 + 4x)

dx

2

2

= 4

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Worksheet by Kuta Software LLC

For each problem, find the area of the region enclosed by the curves. You may use the provided graph to sketch the curves and shade the enclosed region.

5) y = -2x2 - 1 y = -x + 3 x = 0 x = 1

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

1 (-x + 3 - (-2x2 - 1)) dx

0

25 = 4.167

6

6) y = 2 3 x2 y = x

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

8 (2 3 x2 - x) dx

0

32 = = 6.4

5

7) y = -x3 + 6x y = -x2

y 8

6

4

2

-8 -6 -4 -2 -2

2 4 6 8x

-4

-6

-8

0 (-x2 - (-x3 + 6x)) dx +

-2

3 (-x3 + 6x + x2) dx

0

253 = 21.083

12

8) y = -2 sec2 x y = 2cos x x = 0 x = 4

y 4

3

2

1

-

-

2 -1

x

2

-2

-3

-4

4 (2cos x + 2 sec2 x) dx

0

= 2 + 2 3.414

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Worksheet by Kuta Software LLC

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