WILL MAKE YOU THE BRAINEST
Find the area of the region bounded by the curves y equals the inverse sine of x divided by 4, y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

1/30

Step-by-step explanation:

∫[0,4] arcsin(x/4) dx = 2π-4

x = 4sin(u)

arcsin(x/4) = arcsin(sin(u)) = u

dx = 4cos(u) du

∫[0,4] 4u cos(u) du

∫[0,4] f(x) dx = ∫[0,π/2] g(u) du

v = ∫[1,e] π(R^2-r^2) dx

where R=2 and r=lnx+1

v = ∫[1,e] π(4-(lnx + 1)^2) dx

Using shells dy

v = ∫[0,1] 2πrh dy

where r = y+1 and h=x-1=e^y-1

v = ∫[0,1] 2π(y+1)(e^y-1) dy

v = ∫[0,1] (x-x^2)^2 dx = 1/30

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45