What is the integral of a^2sin^2(x) ?

The integral of a^2sin^2(x) is a^2 1/2 (x-1/2 sin(2x))+C

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integral of a^2sin^2(x)

\int a^{2} sin^{2} (x) d x

a^{2} \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

Solution steps

\int a^{2} sin^{2} (x) d x

Take the constant out:

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

= a^{2} \cdot \int sin^{2} (x) d x

Rewrite using trig identities

= a^{2} \cdot \int \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

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

= a^{2} \frac{1}{2} \cdot \int 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= a^{2} \frac{1}{2} (\int 1 d x - \int cos (2 x) d x)

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

= a^{2} \frac{1}{2} (x - \frac{1}{2} sin (2 x))

Add a constant to the solution

= a^{2} \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

\int (3 x - 2) sin (1 - x) d x

\int \frac{3 x}{2 x ^{2} - 6} d x

\int \frac{1}{( 3 x + 4 ) ^{3}} d x

\int x x^{2} - 25 d x

What is the integral of a^2sin^2(x) ?
The integral of a^2sin^2(x) is a^2 1/2 (x-1/2 sin(2x))+C