What is the integral from 0 to sqrt(pi of)5xcos(x^2) ?

The integral from 0 to sqrt(pi of)5xcos(x^2) is 0

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integral from 0 to sqrt(pi of)5xcos(x^2)

\int_{0}^{π} 5 x cos (x^{2}) d x

0

Solution steps

\int_{0}^{π} 5 x cos (x^{2}) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{π} x cos (x^{2}) d x

Apply u-substitution

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

= 5 \cdot \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

= 5 \cdot \frac{1}{2} \cdot \int_{0}^{π} cos (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{2} [sin (u)]_{0}^{π}

Simplify

5 \cdot \frac{1}{2} [sin (u)]_{0}^{π} : \frac{5}{2} [sin (u)]_{0}^{π}

= \frac{5}{2} [sin (u)]_{0}^{π}

Compute the boundaries:

0

= \frac{5}{2} \cdot 0

Simplify

= 0

n = 1 \sum \infty \frac{e ^{n}}{n !}

y^{^{''}} + 16 y = 16 cos (4 x)

f (x) = 2 π

\int_{x^{5}}^{x^{3}} (2 t - 1)^{3} d t

\frac{1}{e ^{5 - 2 x}}

What is the integral from 0 to sqrt(pi of)5xcos(x^2) ?
The integral from 0 to sqrt(pi of)5xcos(x^2) is 0