What is the integral from 0 to 2 of sin(Ax) ?

The integral from 0 to 2 of sin(Ax) is (2sin^2(A))/A

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integral from 0 to 2 of sin(Ax)

\int_{0}^{2} sin (A x) d x

\frac{2 sin ^{2} ( A )}{A}

Solution steps

\int_{0}^{2} sin (A x) d x

Apply u-substitution

: \int_{0}^{A \cdot 2} \frac{sin ( u )}{A} d u

= \int_{0}^{A \cdot 2} \frac{sin ( u )}{A} d u

Take the constant out:

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

= \frac{1}{A} \cdot \int_{0}^{A \cdot 2} sin (u) d u

Use the common integral:

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

= \frac{1}{A} [- cos (u)]_{0}^{A \cdot 2}

Compute the boundaries:

2 sin^{2} (A)

= \frac{1}{A} \cdot 2 sin^{2} (A)

Simplify

= \frac{2 sin ^{2} ( A )}{A}

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What is the integral from 0 to 2 of sin(Ax) ?
The integral from 0 to 2 of sin(Ax) is (2sin^2(A))/A