What is the integral from x to 4 of sin(t^2) ?

The integral from x to 4 of sin(t^2) is sqrt(pi/2)\S(sqrt(2/pi)*4)-sqrt(pi/2)\S(sqrt(2/pi)x)

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integral from x to 4 of sin(t^2)

\int_{x}^{4} sin (t^{2}) d t

\frac{π}{2} § (\frac{2}{π} \cdot 4) - \frac{π}{2} § (\frac{2}{π} x)

Solution steps

\int_{x}^{4} sin (t^{2}) d t

Use the nonelementary integral:

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

= [\frac{π}{2} § (\frac{2}{π} t)]_{x}^{4}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 4) - \frac{π}{2} § (\frac{2}{π} x)

= \frac{π}{2} § (\frac{2}{π} \cdot 4) - \frac{π}{2} § (\frac{2}{π} x)

\int_{0}^{y} \frac{x}{y} d x

\int_{1}^{2} \frac{10 - 3 x}{x ^{3}} d x

\int_{0}^{1} π (1 - x)^{2} d x

\int_{0}^{\frac{π}{2}} cos^{4} (t) d t

\int_{0}^{2 π} x ∣ sin (x) ∣ d x

What is the integral from x to 4 of sin(t^2) ?
The integral from x to 4 of sin(t^2) is sqrt(pi/2)\S(sqrt(2/pi)*4)-sqrt(pi/2)\S(sqrt(2/pi)x)