What is the integral from-1 to 2 of |x-1|sin(x) ?

The integral from-1 to 2 of |x-1|sin(x) is -3sin(1)+2cos(1)-cos(2)+sin(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 2 of |x-1|sin(x)

\int_{- 1}^{2} ∣ x - 1 ∣ sin (x) d x

- 3 sin (1) + 2 cos (1) - cos (2) + sin (2)

Decimal

- 0.11836 \dots

Solution steps

\int_{- 1}^{2} ∣ x - 1 ∣ sin (x) d x

Eliminate Absolutes

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

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

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

= - 2 sin (1) + 2 cos (1) - cos (2) + sin (2) - sin (1)

Simplify

= - 3 sin (1) + 2 cos (1) - cos (2) + sin (2)

What is the integral from-1 to 2 of |x-1|sin(x) ?
The integral from-1 to 2 of |x-1|sin(x) is -3sin(1)+2cos(1)-cos(2)+sin(2)