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

The integral from 1 to 2 of sin(sqrt(x-1)) is 2(sin(1)-cos(1))

Popular >

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

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

2 (sin (1) - cos (1))

Decimal Notation

0.60233 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{1} sin (u) \cdot 2 u d u

= \int_{0}^{1} sin (u) \cdot 2 u d u

Take the constant out:

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

= 2 \cdot \int_{0}^{1} sin (u) u d u

Apply Integration By Parts

: [- u cos (u) - \int - cos (u) d u]_{0}^{1}

= 2 [- u cos (u) - \int - cos (u) d u]_{0}^{1}

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

= 2 [- u cos (u) - (- sin (u))]_{0}^{1}

Simplify

= 2 [- u cos (u) + sin (u)]_{0}^{1}

Compute the boundaries:

sin (1) - cos (1)

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

\int_{1}^{5} 1 + (\frac{1}{x})^{2} d x

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

\int_{0}^{1} x^{6} e^{x} d x

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

\int_{- 2}^{- 1} e^{- x} d x

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