Name _ Date _ Period _ AP Calculus AB
2 1. Using 4 intervals approximate the definite integral, x dx , (area under the curve, Riemann Sum) by using 0 4
the left, right, midpoint, and trapezoid method. Round your answer to three decimal places. 2. Using 4
Name _ Date _ Period _ AP Calculus AB
10
1. Approximate the definite integral (area under the curve, Riemann Sum) of
x
2 8
2
dx with 4 subintervals using
the left, right, trapezoid and midpoint method. Round your answer to three decimal places. 2. Approxi
Name _ Date _ Period _ Calculus B The graph of a function f consists of a semicircle and two line segments as shown below. Let h be the function given by h ( x ) = f ( t ) dt . Compute the following values.
0 x
y 10 9 8 7 6 5 4 3 2 1 -10-9 -8 -7 -6 -5 -4
Name _ Date _ Period _ Calculus B Solve for y by the method of separation of variables. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. dy = 3y ; y(0) = 2 dx dy = 2 y ; y(0) = 10 dt dy 4 xy = 0 ; y(0) = 5 dx dy + y = 0 ; y(0) = 4 dt dy + y = 0
Name _ Date _ Period _ Calculus B Solve the initial value problems. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. dy dx dy dx dy dx dy dx dy dx dy dx dy dt dy dx dy dx = 4 x 3 + 2 x ; y(2) = 1 = 1 x ; y(1) = 3 x
= cos x + sec 2 x ; y(0) = = 4 sin x + 2 cos x ; y( ) = -2
Approximating the Definite Integral (The Area Under a Curve, Riemann Sum)
Thus far we have explored the Definite Integral,
f (x)dx .
a
b
We will now learn how to approximate the Definite Integral (the area under the curve, Riemann Sum) which has the for
Name _ Date _ Period _ Calculus B Use the initial conditions to solve each problem. 1. There is initially a colony of 500 bacteria on a rotting piece of meat. The population b grows according to db = kb , where k is a constant and t is measured in hours.
Syllabus for Math 1A, Fall 2014, Ole Haid, MWF 2-3 in Dwinelle 155.
Office Hours M 12-1, W 12:30-1 :30, F 3:304:30 in 875 Evans Hall. Home works (worth
15% of your grade) are due in discussion hours, on the date given below. i will drop
your 3 lowest scor