What is the integral from 2 to 5 of (cos(x/(10))) ?

The integral from 2 to 5 of (cos(x/(10))) is 10(sin(1/2)-sin(1/5))

Popular >

integral from 2 to 5 of (cos(x/(10)))

\int_{2}^{5} (cos (\frac{x}{10})) d x

10 (sin (\frac{1}{2}) - sin (\frac{1}{5}))

Decimal

2.80756 \dots

Solution steps

\int_{2}^{5} cos (\frac{x}{10}) d x

Apply u-substitution

: \int_{\frac{1}{5}}^{\frac{1}{2}} cos (u) \cdot 10 d u

= \int_{\frac{1}{5}}^{\frac{1}{2}} cos (u) \cdot 10 d u

Take the constant out:

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

= 10 \cdot \int_{\frac{1}{5}}^{\frac{1}{2}} cos (u) d u

Use the common integral:

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

= 10 [sin (u)]_{\frac{1}{5}}^{\frac{1}{2}}

Compute the boundaries:

sin (\frac{1}{2}) - sin (\frac{1}{5})

= 10 (sin (\frac{1}{2}) - sin (\frac{1}{5}))

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

\int_{0}^{3} (3 t - 1)^{58} d t

\int_{0}^{t} \frac{1}{x ^{2}} d x

\int_{1}^{4} 21 x^{\frac{5}{2}} d x

\int_{1}^{2.5} \frac{3}{2 x ^{2}} d x

What is the integral from 2 to 5 of (cos(x/(10))) ?
The integral from 2 to 5 of (cos(x/(10))) is 10(sin(1/2)-sin(1/5))