What is the integral from-0.5 to 1 of cos(x^2) ?

The integral from-0.5 to 1 of cos(x^2) is 1.25331…\C(sqrt(2/pi)*1)-1.25331…\C(-0.5sqrt(2/pi))

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integral from-0.5 to 1 of cos(x^2)

\int_{- 0.5}^{1} cos (x^{2}) d x

1.25331 \dots C (\frac{2}{π} \cdot 1) - 1.25331 \dots C (- 0.5 \frac{2}{π})

Solution steps

\int_{- 0.5}^{1} cos (x^{2}) d x

Use the nonelementary integral:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= [\frac{π}{2} C (\frac{2}{π} x)]_{- 0.5}^{1}

Simplify

= [1.25331 \dots C (\frac{2}{π} x)]_{- 0.5}^{1}

Compute the boundaries:

1.25331 \dots C (\frac{2}{π} \cdot 1) - 1.25331 \dots C (- 0.5 \frac{2}{π})

= 1.25331 \dots C (\frac{2}{π} \cdot 1) - 1.25331 \dots C (- 0.5 \frac{2}{π})

\frac{d y}{d x} = \frac{y}{x} + 6 x + 7

x \to 4 lim (\frac{2 x + 8}{x - 4})

\frac{d}{d x} (\frac{e ^{x}}{2 x - 1})

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

\frac{d}{d x} (\frac{e ^{x} - 1}{2 x})

What is the integral from-0.5 to 1 of cos(x^2) ?
The integral from-0.5 to 1 of cos(x^2) is 1.25331…\C(sqrt(2/pi)*1)-1.25331…\C(-0.5sqrt(2/pi))