Question

Integration of Cos root x by root x dx ​

Answer 1

Answer:

solved

Step-by-step explanation:

N = Integration of Cos root x by root x dx ​ = ∫  (Cos√ x /√ x )dx

let √x = u

dx/2√x = du

dx = 2udu

N = ∫  (Cos√ x /√ x )dx = ∫ cosu/u . 2udu = 2∫cosudu = - 2 sinu + c

= - 2 sin√x + c

Answer 2

Answer:

The given integral is

$I = ∫ \frac{cos \sqrt{x} }{ \sqrt{x} } dx = 2sin{\sqrt{x} }+ c$

Step-by-step explanation:

The Given integral is as follows

$I = ∫ \frac{cos \sqrt{x} }{ \sqrt{x} } dx$

This can be found out by simple substitution.

The substitution is as follows

$\sqrt{x} = t \\ \frac{1}{2 \sqrt{x} } dx = dt \\ dx = 2 \sqrt{x} dt = 2t.dt$

Substituting the above terms in given integral we get as follows

$I = ∫ \frac{cost}{t} (2t.dt) = 2∫cost.dt \\ = 2sint + c$

Therefore the given integral is

$I = ∫ \frac{cos \sqrt{x} }{ \sqrt{x} } dx = 2sin{\sqrt{x}} + c$

(Here c is integration constant)

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