- #1

- 17

- 0

[tex]

\int_{1}^{x^2} \sin{(\sqrt{t})} \ dt

[/tex]

- Thread starter SplinterIon
- Start date

- #1

- 17

- 0

[tex]

\int_{1}^{x^2} \sin{(\sqrt{t})} \ dt

[/tex]

- #2

MalleusScientiarum

Try making a u-substitution for the square root of t.

- #3

- 970

- 3

The closest identity that I could determine is:

identity:

[tex]\int u \sin u \; du = \sin u - u \cos u + C[/tex]

[tex]\int \sin \sqrt{t} \; dt = 2 \left( \sin \sqrt{t} - \sqrt{t} \cos \sqrt{t} \right) + C[/tex]

- #4

HallsofIvy

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Good try but it looks to me like that gives youMalleusScientiarum said:Try making a u-substitution for the square root of t.

[tex]\int u^{\frac{1}{2}}sin u du[/tex] which doesn't look any more hopeful.

I'd be willing to bet that this doesn't have an elementary anti-derivative.

- #5

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[tex] \sqrt{t}=u [/tex]

implies [itex] t=u^{2} \ \mbox{and} \ dt= 2 u du [/itex]

and the antiderivative becomes

[tex] \int 2 u \sin u \ du [/tex] which can be easily tackled with the part integration method.

Daniel.

- #6

HallsofIvy

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One of these days, I really have to learn algebra!

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