Consider the region bounded by y = ex, y = 4, and x = 0 . a solid is created so that the given region is its base and cross-sections perpendicular to the y-axis are squares. set up a riemann sum and then a definite integral needed to find the volume of the solid. what is the approximate volume of a slice perpendicular to the y-axis? you can type the word delta or use the calcpad when you need δ. (ln(y)2)δy in your definite integral what is the lower endpoint? 0 in your definite integral what is the upper endpoint? 1 evaluate the integral. give an exact answer.

Each cross section has side length equal to satisfying , where so that .

The exact volume is given by the definite integral,

Take a slice at any value of with thickness . Then the slice has volume .

The approximate total volume of these slices is then given by the Riemann sum,

where are chosen however you like from the range above.

Compute the definite integral above for the exact volume: you can do this by parts, taking

The remaining integral can be done by parts again, this time with

and of course

So we have

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752