Question

Evaluate the integral by making the given substitution

Answer 1

\[\int\limits_{?}^{?}(2\sin(\sqrt{x}))\div \sqrt{x} u=\sqrt{x}\]

Answer 2

What's the given substitution?

Answer 3

u=sqrt (x)

Answer 4

u=sqrt(x)

Answer 5

you get integral sin(u) du

Answer 6

= -cos(sqrt(x) ) + constant

Answer 7

nah i think thats wrong

Answer 8

was doing too many steps in my head I think

Answer 9

there should be a 4


-4cos( sqrt(x)) +C

Answer 10

differentiate that and it works out

Answer 11

where did you get the -4?

Answer 12

2sin(sqrt(x))
{S} ---------- dx ; u = sqrt(x)
sqrt(x)

Dx(u = sqrt(x))

du = 1/2sqrt(x) dx

dx = 2sqrt(x) du ; but since u = sqrt(x) we get:

dx = 2u du
................................


2 sin(u) 2u
{S} --------- du ; the u up top and bottom cancel
u


{S} 2 sin(u) 2 du ; now 2*2 = 4 so rewrite as:

{S} 4 sin(u) du ; pull out the constant (4)

4 {S} sin(u) du and integrate

Answer 13

sin(u) integrates up to -cos(u) soo...

4 (-cos(u)) + C

-4 cos(sqrt(x)) + C