What is the integral from 0 to 1 of 10cos(x^2) ?

The integral from 0 to 1 of 10cos(x^2) is 10(sqrt(pi/2)\C(sqrt(2/pi)*1)-sqrt(pi/2)\C(sqrt(2/pi)*0))

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integral from 0 to 1 of 10cos(x^2)

\int_{0}^{1} 10 cos (x^{2}) d x

10 (\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0))

Solution steps

\int_{0}^{1} 10 cos (x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{0}^{1} cos (x^{2}) d x

Use the nonelementary integral:

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

= 10 [\frac{π}{2} C (\frac{2}{π} x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= 10 (\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0))

\int (x + 3) (x - 5) d x

\int_{2}^{6} \frac{1}{3 x - 2} d x

\frac{d}{d t} (2 cos (t) + 2 sin (t))

F (x) = (9 x^{6} + 4 x^{3})^{4}

y^{^{''}} - 2 y^{^{'}} - 3 y = 16 x^{2} e^{- x}

What is the integral from 0 to 1 of 10cos(x^2) ?
The integral from 0 to 1 of 10cos(x^2) is 10(sqrt(pi/2)\C(sqrt(2/pi)*1)-sqrt(pi/2)\C(sqrt(2/pi)*0))