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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{0}^{π} x \cdot 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

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{4}} d x

\int_{- \frac{1}{8}}^{\frac{1}{8}} (sin (2 π x)) d x

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

\int_{0}^{60} \frac{x}{2} d x

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

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