- #1

dwdoyle8854

- 16

- 0

## Homework Statement

I've run into this problem a few times, where I get the right answer, but multiplied by a constant where I would have it divided by the constant or vice versa.

"First make a substitution and then use integration by parts to evaluate the integral"

∫cos(√x)dx

## Homework Equations

∫udv = uv - ∫vdu

## The Attempt at a Solution

let A = √x

dA = dx/(2√x)

2(√x)dA = dx

A

^{2}= x

2∫Acos(A)dA

let u=A

du=dA

dv= cos(A)

v = sin A + C

2∫Acos(A)dA = Asin(A) - ∫sin(A)

= Asin(A) + cos(A)

so, then

∫Acos(A)dA = (Asin(A) +cos(A))/2 +C

this is wrong, it should be 2Asin(A) + 2cos(A) + C and I am not sure where exactly I can remedy this.

I think my problem might be with 2∫Acos(A)dA = Asin(A) - ∫sin(A)

since I have an integral I am evaluating by parts multiplied by a constant, does

2∫Acos(A)dA = Asin(A) - ∫sin(A) => 2∫Acos(A)dA = 2(Asin(A) - ∫sin(A)) ?

or more generally c∫udv = c(uv - ∫vdu) ?