Are You Smarter
Than A Calculus
Teacher?
• Integrals
• Integrals
• Area
• Area
• Derivatives
• Derivatives
• Integrals Hard
• Integrals Hard
• Optimization
Problems
• Optimization
Problems
Integrals
• Evaluate
5
𝑑𝑥 .
3
(5−4𝑥)
Integrals
• Evaluate
7 2 3
𝑥
3
𝑥 3 − 5 𝑑𝑥.
Area
• Use upper and lower sums to
find the area bounded by the
x-axis and x = 1 to x = 5, using 8
2
rectangles, for 𝑦 = 𝑥 − 1.
Area
• Use the trapezoidal rule and
Simpson’s rule with n = 4 to
6 2
approximate 2 𝑥 − 1.
Derivatives
• Find the derivative of
𝑦=
𝑥(𝑥−1)
𝑙𝑛
.
𝑥−2
Derivatives
• Find the derivative of
−𝑐𝑜𝑠3𝑥
𝑦=𝑒
(𝑠𝑖𝑛4𝑥)
Integrals Hard
• Find the indefinite integral of
𝑒 2𝑥 −𝑒 −2𝑥
𝑑𝑥.
2𝑥
−2𝑥
𝑒 +𝑒
Integrals Hard
• Find the indefinite integral of
4𝑥
4 𝑑𝑥.
25+4𝑥
Optimization Problems
• Find the dimensions of the window below
to maximize the area of the rectangular
region if the total perimeter of the whole
window is 16 feet.
Optimization Problems
• I want to plant a garden at my house.
One side will be up against the house
so it will not need fencing. If I have 325
feet of fence what should the
dimensions of my garden be to
maximize my area for my garden?