What is the integral from 0 to 0.2 of sin^2(x) ?

The integral from 0 to 0.2 of sin^2(x) is 0.00264…

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integral from 0 to 0.2 of sin^2(x)

\int_{0}^{0.2} sin^{2} (x) d x

0.00264 \dots

Solution steps

\int_{0}^{0.2} sin^{2} (x) d x

Rewrite using trig identities

= \int_{0}^{0.2} \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

= \frac{1}{2} \cdot \int_{0}^{0.2} 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

= \frac{1}{2} (\int_{0}^{0.2} 1 d x - \int_{0}^{0.2} cos (2 x) d x)

\int_{0}^{0.2} 1 d x = 0.2

\int_{0}^{0.2} cos (2 x) d x = 0.19470 \dots

= \frac{1}{2} (0.2 - 0.19470 \dots)

Simplify

\frac{1}{2} (0.2 - 0.19470 \dots) : 0.00264 \dots

= 0.00264 \dots

\int_{0}^{3} x^{2} - 4 x + 4 d x

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\int_{- 1}^{1} (- x^{2} - 2 x + 8) d x

\int_{- 3}^{2} - y^{2} - y + 6 d y

What is the integral from 0 to 0.2 of sin^2(x) ?
The integral from 0 to 0.2 of sin^2(x) is 0.00264…