What is the integral from 0 to arctan(3) of sin(2x) ?

The integral from 0 to arctan(3) of sin(2x) is 9/10

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integral from 0 to arctan(3) of sin(2x)

\int_{0}^{a r c t a n (3)} sin (2 x) d x

\frac{9}{10}

Decimal

0.9

Solution steps

\int_{0}^{a r c t a n (3)} sin (2 x) d x

Apply u-substitution

: \int_{0}^{2 a r c t a n (3)} sin (u) \frac{1}{2} d u

= \int_{0}^{2 a r c t a n (3)} 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_{0}^{2 a r c t a n (3)} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{0}^{2 a r c t a n (3)}

Compute the boundaries:

\frac{9}{5}

= \frac{1}{2} \cdot \frac{9}{5}

Simplify

= \frac{9}{10}

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\int_{0}^{0.5} \frac{1}{1 - x} d x

What is the integral from 0 to arctan(3) of sin(2x) ?
The integral from 0 to arctan(3) of sin(2x) is 9/10