What is the integral from 0.8 to 1.6 of sin(2x) ?

The integral from 0.8 to 1.6 of sin(2x) is 0.48454…

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integral from 0.8 to 1.6 of sin(2x)

\int_{0.8}^{1.6} sin (2 x) d x

0.48454 \dots

Solution steps

\int_{0.8}^{1.6} sin (2 x) d x

Apply u-substitution

: \int_{1.6}^{3.2} sin (u) \frac{1}{2} d u

= \int_{1.6}^{3.2} sin (u) \frac{1}{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_{1.6}^{3.2} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{1.6}^{3.2}

Simplify

= 0.5 [- cos (u)]_{1.6}^{3.2}

Compute the boundaries:

0.96909 \dots

= 0.5 \cdot 0.96909 \dots

Simplify

= 0.48454 \dots

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What is the integral from 0.8 to 1.6 of sin(2x) ?
The integral from 0.8 to 1.6 of sin(2x) is 0.48454…