Joyce Smith

Answered

2022-01-07

Evaluate the indefinite integral.

$\int \frac{\mathrm{cos}\sqrt{t}}{\sqrt{t}}$

Answer & Explanation

Maria Lopez

Expert

2022-01-08Added 32 answers

Step 1

We have the given integral as

$I=\int \frac{\mathrm{cos}\sqrt{t}}{\sqrt{t}}$

Let us consider that,

$\sqrt{t}=u$

$\frac{1}{2\sqrt{t}}dt=du$

$\frac{1}{\sqrt{t}}dt=2du$

Step 2

On substituting$\sqrt{t}=u$ and $\frac{1}{\sqrt{t}}dt=2du$ in our integral $I=\int \frac{\mathrm{cos}\sqrt{t}}{\sqrt{t}}dt$ , we get the result as

$I=\int 2\mathrm{cos}\left(u\right)du$

$I=2\int \mathrm{cos}\left(u\right)du$

$I=2\mathrm{sin}u+C$

On substituting back$u=\sqrt{t}$ , our integral becomes as

$I=2\mathrm{sin}\left(\sqrt{t}\right)+C$

Hence, value of$I=\int \frac{\mathrm{cos}\sqrt{t}}{\sqrt{t}}dt$ is $I=2\mathrm{sin}\left(\sqrt{t}\right)+C$ .

We have the given integral as

Let us consider that,

Step 2

On substituting

On substituting back

Hence, value of

vicki331g8

Expert

2022-01-09Added 37 answers

put

karton

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