What is the integral from 0 to x^4 of cos(t^2) ?

The integral from 0 to x^4 of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)x^4)-sqrt(pi/2)\C(sqrt(2/pi)*0)

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integral from 0 to x^4 of cos(t^2)

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

\frac{π}{2} C (\frac{2}{π} x^{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

Solution steps

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

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} t)]_{0}^{x^{4}}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} x^{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= \frac{π}{2} C (\frac{2}{π} x^{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

(2, 5), (7, 3)

\int (x^{\frac{1}{2}} + 3 x + 2) d x

θ \to 0 lim (θ cos (θ))

\int \frac{( ln ^{2} ( 3 x ) )}{x} d x

f (x) = \frac{x}{1 + x ^{2}}

What is the integral from 0 to x^4 of cos(t^2) ?
The integral from 0 to x^4 of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)x^4)-sqrt(pi/2)\C(sqrt(2/pi)*0)