Math 1210-001
Homework 9
Due 22 July, 2013
This homework assignment is designed to go along with sections 4.2 through
4.5 of your textbook, which we have completed in class. Make sure your work
is neat, legible, well-organized and self-explanatory. You must staple your
assignment to receive full credit.
Name:
R5
1. (10 points) Use the definition of the definite integral to calculate 0 (x + 1) dx.
R1
R2
R1
R2
2. (10 points) Given that 0 f (x) dx = 3, 1 f (x) dx = −2, 0 g(x) dx = 10, and 1 g(x) dx = 3,
R0
calculate 2 [g(x) − f (x)] dx by first writing the desired integral in terms of the given
integrals, and then substituting the given values.
Z 3
x2 + 1
√
3. (10 points) Calculate
dx.
x3 + 3x
1
Z π
(sin x + cos x) dx. (A direct computation will
4. (10 points) Use symmetry to evaluate
−π
receive no more than 5 points.)
5. (10 points) Find the average value of f (x) = tan x sec2 x on the interval [0, π4 ].