04/19/23 Perkins

AP Calculus AB

Day 2Section 7.1

1. Find the area of the region on bounded by sin2 and cos .f x x g x x

sin2 cosx x2sin cos cosx x x

2sin cos cos 0x x x cos 2sin 1 0x x

12cos 0 sinx x

52 6 6,x x

1

-1

2

2

6

sin2 cosA x x dx

5

6

2

cos sin2x x dx

2u x2du dx

2

6

12 cos2 sinx x

56

2

12sin cos2x x

1 1 1 1 1 12 4 2 2 4 21 1

1 14 4

1

2

5,

6 6

2. Find the area of the triangle with vertices A(2,-3), B(4,6), and C(6,1).

4

2

A AB AC dx 6

4

2

-2

-4

-6

5

C

B

A

6

4

BC AC dx 6 3 9

4 2 2mAB

1 31

6 2mAC

1 6 5

6 4 2mBC

AB 926 4y x 92 12y x

AC 1 1 6y x 5y x

BC 526 4y x 52 16y x

4

92

2

12 5x x dx 6

52

4

16 5x x dx

4 6

7 72 2

2 4

7 21x dx x dx

4 62 27 74 42 4

7 21x x x x

28 28 7 14 63 186 28 84

7 7

14

Perkins

AP Calculus AB

Day 2Section 7.1

1. Find the area of the region on bounded by sin2 and cos .f x x g x x

5,

6 6

2. Find the area of the triangle with vertices A(2,-3), B(4,6), and C(6,1).

6

4

2

-2

-4

-6

5

C

B

A