Name _____________________________ AB Calculus

Applications of Differential Equations Evaluate the indefinite integral.

1. dxx 3 2 2. dxxx

1

3. dxx32

1 4.

dxx 32

1

5. dxx 23 6.

dxxx 122

3

7.

dxx

xx 12

8. dxxx 231

9. dyyy 2 10. dx

11. dxxx cos3sin2 12. dttt cotcsc1

13. dsinsec2 14. dyy 1tan 2

Find the general solution of the differential equation and check the result by differentiation.

15. 23tdt

dy 16. 2

3

xdx

dy

The graph of the derivative of a function is given. Sketch the graphs of TWO functions that have the given derivative. (There is more than one correct answer.) 17. 18. Find the equation for y, given the derivative and the indicated point on the curve.

19. 12 xdx

dy 20. x

dx

dycos

21. A particle moves along the x-axis at a velocity of 0,1

tt

tv . At time t = 1, its

position is x = 4. Find the acceleration and position functions for the particle. 22. The maker of a certain automobile advertises that it takes 13 seconds to accelerate from 25 km/h to 80 km/h. Assuming constant acceleration, compute the following: a) The acceleration in meters per second per second. b) The distance the car travels during the 13 seconds.

6.1 Challenge Problem Name: ______________________ Date: ___________ An upside down pyramid is initially full of water. The height of the pyramid is 10 feet. The base of the pyramid is 3 feet by 3 feet. The rate at which the water is draining out of the

container is 0.4 h . Write an equation for the volume of the water at any given time t. How much water is in the tank at t = 2?