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}

\int_{- 1}^{1} (1 + x) e^{x} d x

\int_{0}^{2} 2 y - y^{2} + 4 d y

\int_{- 3}^{2} x + 3 d x

\int_{1}^{11} (2 x - 12)^{9} d x

\int_{0}^{a} e^{7 x} d x

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