What is the integral from 0 to sqrt(pi of)xcos(x^2) ?

The integral from 0 to sqrt(pi of)xcos(x^2) is 0

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integral from 0 to sqrt(pi of)xcos(x^2)

\int_{0}^{π} x cos (x^{2}) d x

0

Solution steps

\int_{0}^{π} x cos (x^{2}) d x

Apply u-substitution

: \int_{0}^{π} \frac{cos ( u )}{2} d u

= \int_{0}^{π} \frac{cos ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{π} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{2} [sin (u)]_{0}^{π}

Compute the boundaries:

0

= \frac{1}{2} \cdot 0

Simplify

= 0

t^{3} y^{^{'}} + 4 t^{2} y = e^{- t}

n = 1 \sum \infty \frac{1}{( n + 1 ) !}

\int 2 y + x e^{x y} d y

\frac{d}{d x} (\frac{1}{( x + 3 ) ^{5}})

y^{^{''}} + 2 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the integral from 0 to sqrt(pi of)xcos(x^2) ?
The integral from 0 to sqrt(pi of)xcos(x^2) is 0