Calc Midterm 1

Question 1

Integral Notation

Answer 1

∫f(x)dx = F(x) + c

Question 2

Parts of Integral Notation

Answer 2

∫ = integral sign
f(x) = integrand
d(x) = Variable of integration “differential”
F(x) = Antiderivative
c = constant

Question 3

d/dx [sec(x)] = sec(x)tan(x)

Answer 3

∫sec(x)tan(x)dx = sec(x) + c

Question 4

Maybe review properties of integrals

Answer 4

Aye Aye captain

Question 5

Width of each subinterval

Answer 5

delta x = (b-a)/n

Question 6

Height of each subinterval

Answer 6

f(x*n)

Question 7

Rectangle area notation

Answer 7

A = lim ∑ f(x*k)delta x
n->∞

n on top
k=1

THE ACTUAL AREA IS THE LIMIT OF THE AREAS OF THE RECTANGLES

Question 8

LRAM tends to
RRAM tends to
MRAM tends to be

Answer 8

Overapproximate
Underapproximate
Somewhere in the middle

Question 9

Trapezoid area

Answer 9

A = 1/2h(b1+b2)

Question 10

Tn

Answer 10

1/2(b-a/n)(Yo + 2Y1 + …2Yn-1 + Yn)

Question 11

∑ f(x*k)delta xk

n on top
k=1

Answer 11

Rimman Sum

Question 12

What is a definite intergral?

Answer 12

The limit of a rimman sum

Question 13

Definite integral notation

Answer 13

∫ f(x)dx
b upper limit of integration
a lower limit of integration

“The integral from a to b of f(x)dx

Question 14

FTC Part one definition

Answer 14

∫ f(x)dx = f(b) - f(a)
b upper limit of integration
a lower limit of integration

NO C BECAUSE ITS DEFINITE

Question 15

Always do work

Answer 15

down

Question 16

Remember the chain rule

Answer 16

Aye Aye captain

Question 17

Review the unit circle and derivatives

Answer 17

Aye Aye captain