What is the integral from 0 to sqrt(3pi of)xcos(x^2) ?

The integral from 0 to sqrt(3pi of)xcos(x^2) is 0

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integral from 0 to sqrt(3pi of)xcos(x^2)

\int_{0}^{3 π} x cos (x^{2}) d x

0

Solution steps

\int_{0}^{3 π} x cos (x^{2}) d x

Apply u-substitution

: \int_{0}^{3 π} \frac{cos ( u )}{2} d u

= \int_{0}^{3 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}^{3 π} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{3 π}

Compute the boundaries:

0

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

Simplify

= 0

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

\int_{\frac{y}{2}}^{1} e^{x^{2}} d x

\int_{0}^{2} \frac{3 x}{( x ^{2} + 1 ) ^{2}} d x

\int_{0}^{π} [x] sin (x) d x

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

What is the integral from 0 to sqrt(3pi of)xcos(x^2) ?
The integral from 0 to sqrt(3pi of)xcos(x^2) is 0