What is the integral from pi/2 to sqrt(x of)sin(15t) ?

The integral from pi/2 to sqrt(x of)sin(15t) is -1/15 cos(15sqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from pi/2 to sqrt(x of)sin(15t)

\int_{\frac{π}{2}}^{x} sin (15 t) d t

- \frac{1}{15} cos (15 x)

Solution steps

\int_{\frac{π}{2}}^{x} sin (15 t) d t

Apply u-substitution

: \int_{\frac{15 π}{2}}^{15 x} sin (u) \frac{1}{15} d u

= \int_{\frac{15 π}{2}}^{15 x} sin (u) \frac{1}{15} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int_{\frac{15 π}{2}}^{15 x} sin (u) d u

Use the common integral:

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

= \frac{1}{15} [- cos (u)]_{\frac{15 π}{2}}^{15 x}

Compute the boundaries:

- cos (15 x)

= \frac{1}{15} (- cos (15 x))

Simplify

= - \frac{1}{15} cos (15 x)

\int_{0}^{8} \frac{x}{8} d x

\int_{1}^{2} \frac{5}{t} d t

\int_{- 1}^{2} [x] d x

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

\int_{0}^{2 π} 3 cos (t) d t

What is the integral from pi/2 to sqrt(x of)sin(15t) ?
The integral from pi/2 to sqrt(x of)sin(15t) is -1/15 cos(15sqrt(x))