What is the integral from 1 to 6 of sin(4x+2.8) ?

The integral from 1 to 6 of sin(4x+2.8) is 0.24142…

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integral from 1 to 6 of sin(4x+2.8)

\int_{1}^{6} sin (4 x + 2.8) d x

0.24142 \dots

Solution steps

\int_{1}^{6} sin (4 x + 2.8) d x

Apply u-substitution

= \int_{6.8}^{26.8} sin (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{6.8}^{26.8} sin (u) d u

Use the common integral:

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

= \frac{1}{4} [- cos (u)]_{6.8}^{26.8}

Simplify

= 0.25 [- cos (u)]_{6.8}^{26.8}

Compute the boundaries:

0.96571 \dots

= 0.25 \cdot 0.96571 \dots

Simplify

= 0.24142 \dots

What is the integral from 1 to 6 of sin(4x+2.8) ?
The integral from 1 to 6 of sin(4x+2.8) is 0.24142…