What is the integral from 0 to t of sin(x^2) ?

The integral from 0 to t of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)t)-sqrt(pi/2)\S(sqrt(2/pi)*0)

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integral from 0 to t of sin(x^2)

\int_{0}^{t} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} t) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{t} sin (x^{2}) d x

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= [\frac{π}{2} § (\frac{2}{π} x)]_{0}^{t}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} t) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} t) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\int_{- 2}^{- 1} 3 x - 9 d x

\int_{- π}^{π} x cos (n) x d x

\int_{0}^{s i n (z)} x - 1 d x

\int_{\frac{π}{4}}^{\frac{3 π}{4}} csc (x) d x

\int_{1}^{2} \frac{2 x}{( x ^{2} + 1 ) ^{2}} d x

What is the integral from 0 to t of sin(x^2) ?
The integral from 0 to t of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)t)-sqrt(pi/2)\S(sqrt(2/pi)*0)