Solve this indefinite integral:

I am offering 50 points for this question.

2 ( x sin x + cos x) + c  where c is the constant of integration

Step-by-step explanation:

∫ 2x cos x dx

2 ∫ x cos x dx

Use integration by parts

u = x     dv = cos x

du = 1     v = sin x

∫ u v =  u v - ∫v du

∫ x cos x dx =  x sinx - ∫ sin x *1

                     = x sin x -  (- cos x)

                      = x sin x + cos x

2 ∫ x cos x dx = 2 ( x sin x + cos x) + c where c is the constant of integration

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get