## Calculus II M142

**Quiz 1.**

Section 5.3:

# 1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 35, 37, 39, 41, 43, 45, 49, 51, 53, 55, 61, 63, 67, 70, 71, 73, 75, 77.

Section 5.1:

# 23, 25, 28, 29, 32, 35, 36, 39, 42.

**Quiz 2.**

Section 5.1:

# 5, 7, 9, 43, 47, 55, 58, 59, 63, 67, 73.

Section 5.2:

# 1, 4, 6, 7, 11, 17, 19, 55, 57, 59, 61, 64, 66.

**Quiz 3.**

Section 5.7:

# 11, 13, 17, 19, 20, 21, 23, 29, 33, 39, 59, 67, 72, 80, 83, 91.

Section 5.8:

# 7, 9, 10, 11, 15, 23, 25, 27, 44, 50.

Section 6.1:# 3, 5, 9, 21, 27, 29, 31, 35, 38, 41, 47.

**Quiz 4.**

Section 6.1:

# 17, 19, 27, 41, 43, .

Section 6.2:

# 1, 2, 3, 5, 9, 11, 13, 16.

**Quiz 5.**

Quiz 4 problems and the examples I uploaded using washer method

(Find the file under section "Examples with Useful Tricks" below.)

**Quiz 6.**

Section 7.1:

# 1,3,7,9,13,21,22,23,35,41,47,48,49,57,77,79.

(You can always check your solution for the odd problems
in the back of the textbook).

**Quiz 7.**

Section 7.2:

# 1, 3, 5, 15, 27, 35, 37, 39, 49, 51, 53, 55.

Section 7.3:

# 1, 4, 6, 7, 9, 15, 17, 19, 21, 48

(You can always check your solution for the odd problems in
the back of the textbook).

**Quiz 8.**

Section 7.4:

# 1, 3, 5, 7, 9, 11.

Section 7.5:

# 5, 7, 9, 11, 31, 37.

(You can always check your solution for the odd problems in
the back of the textbook).

**Quiz 9.**

Section 7.9:

# 7, 11.

Section 8.4:

# 3, 7, 11, 21, 25.

(You can always check your solution for the odd problems in
the back of the textbook).

**Quiz 10.**

Section 10.1:

# 3, 5, 11, 15, 17, 19, 21, 23, 25, 27,
29, 35, 37, 39, 41, 43, 45, 49, 51, 53, 55, 63.

Section 10.2:

# 3, 5, 11, 12, 13, 17.

(You can always check your solution for the odd problems in
the back of the textbook).

**Section 5.3:**

**Section 5.1:**

- Summation Formulas and Sigma Notation (By rootmath)
- Left approximation of area under the curve of $f(x)=x^2+1$
from $x=1$ to $x=3$ using 4 rectangles (By Khan Academy)

- General left approximation, $L_n$, using $n$ rectangles (By Khan Academy)

- Comparison between left, midpoint and right approximations (By Khan Academy)

- Definite integral using limit definition of integrals
$$\int_a^b f(x)\,dx =\lim_{n\to\infty} R_n=\lim_{n\to\infty} \Delta x\cdot\sum_{i=1}^n f(x_i), $$
where $\Delta x=\frac{b-a}{n}$ and $x_i=a+i\,\Delta x$ for $i=1,2,\cdots,n$. (By HM McCormick)

**Section 5.2:**

- Breaking up integral interval (By Khan Academy)
Assume $a\leq b\leq c$, then
$$\int_a^c f(x)\,dx=\int_a^b f(x)\,dx +\int_b^c f(x)\,dx. $$

- Switching bounds of definite integral (By Khan Academy)
$$ \int_b^a f(x)\,dx=-\int_a^b f(x)\,dx.$$

- Evaluating definite integral from graph (using geometry)

similar to problem 7 in section 5.2 (By Khan Academy)

- Definite integrals and negative area (By Khan Academy)

**Section 5.4:**

**Section 5.5:**

**Section 5.6:**

**Section 5.7:**

**Section 5.8:**

**Section 6.1:**

**Section 6.2:**

**Section 6.3:**

**Section 6.4:**

**Section 6.5:**

**Section 7.1:**

**Section 7.2:**

**Section 7.3:**

**Section 7.4:**