What is the integral from 1 to 5 of sin(x^2) ?

The integral from 1 to 5 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*5)-sqrt(pi/2)\S(sqrt(2/pi)*1)

Popular >

integral from 1 to 5 of sin(x^2)

\int_{1}^{5} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} \cdot 5) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

Solution steps

\int_{1}^{5} 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)]_{1}^{5}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 5) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

= \frac{π}{2} § (\frac{2}{π} \cdot 5) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

\int_{0}^{1} 1 + cos (π x) d x

\int_{0}^{π} x^{2} sin (k x) d x

\int_{- 2}^{6} (3 - \frac{x ^{2}}{4} + x) d x

\int_{1}^{4} (3 x^{2} - 2 x + 4) d x

\int_{1}^{2} e^{x} + 2 d x

What is the integral from 1 to 5 of sin(x^2) ?
The integral from 1 to 5 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*5)-sqrt(pi/2)\S(sqrt(2/pi)*1)