TEST2

Area under the curve

100

What is:
1) delta X
2) Xi
In limit of a summation?

b-a/n

a+(deltaX)i

200

Summation i^2

n(n+1)(2n+1)/6

300

What is the formula for Sum to estimate the area under a curve

sum= f(xi) delta x

400

Summation (3i+1)^2

3n^3+15/2 n^2 + 11/2 n

500

for f(x)= 3-2x on the interval [-1,1] find f(mi) and f(Mi)

f(mi)=5-4i/n

f(Mi)=5- (4i+4)/n

definite integral

100

int_a^p f(x) + int_p^b f(x)
write it in just 1 integral

int_a^b f(x)

200

int₂²(ln(x) - e^x +sinh(x)) dx = ?

0

300

lim_n^infSum (2/(xi-4)^2 deltax  over [6,8] =?
write in definite integral form

int₆⁸ (2/(x-4)^2 dx

400

int₀⁴(x^2 - e^x) dx =?

write in reimann sum form and solve

lim_n^inf Sum (xi^2 - e^xi) delta x

67/3 - e^4

500

Find the limit:

lim_n^inf Sum (9i/n . 9/2n)

81/4

FTC

100

g(x) = int_a^xf(t) dt
what is g'(x)

f(x)

200

Give the formula for FTC2 in terms of f(x)

int_a^bf(x)= F(b)-F(a)

300

g(x) = int_a^h(x)f(t) dt
what is g'(x)

f(h(x)). h'(x)

400

f(x) = int_x^3^x sqrt(t) dt
Find f'(x)

-3x^7/2+ sqrt(x)

500

Solve:

int_-5^-1|2x+8| dx 

10

Area Between the curves

100

find bigger function from:

y=2x²

y=x⁴+1

x⁴+1

200

find the point of intersection:
y= x²+3x
y= x+3

x=1
x=-3

300

find the points of intersection
x=y²+1
x=y⁴-2y²-3

y=2

y=-2

400

find area wrt y
y= sqrt(2x+4)

y=x+2

2/3

500

Find the area bounded by:
y=x²+2x+1
y=x-2
between [-1,1]

20/3