What is the integral from 0 to 1 of sin(3pix) ?

The integral from 0 to 1 of sin(3pix) is 2/(3pi)

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integral from 0 to 1 of sin(3pix)

\int_{0}^{1} sin (3 π x) d x

\frac{2}{3 π}

Decimal Notation

0.21220 \dots

Solution steps

\int_{0}^{1} sin (3 π x) d x

Apply u-substitution

: \int_{0}^{3 π} sin (u) \frac{1}{3 π} d u

= \int_{0}^{3 π} sin (u) \frac{1}{3 π} d u

Take the constant out:

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

= \frac{1}{3 π} \cdot \int_{0}^{3 π} sin (u) d u

Use the common integral:

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

= \frac{1}{3 π} [- cos (u)]_{0}^{3 π}

Compute the boundaries:

2

= \frac{1}{3 π} \cdot 2

Simplify

= \frac{2}{3 π}

y = 6 x - 11

\int (\frac{5}{x} + sec^{2} (x)) d x

\frac{d}{d x} (- e^{x} sin (x) + e^{x} cos (x))

x \to 2 lim (3.5 + 5.6)

x \to 2 - lim (\frac{2 - ∣ x ∣}{2 + x})

What is the integral from 0 to 1 of sin(3pix) ?
The integral from 0 to 1 of sin(3pix) is 2/(3pi)