What is the integral from-1 to 1 of cos^2(x) ?

The integral from-1 to 1 of cos^2(x) is 1+1/2 sin(2)

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integral from-1 to 1 of cos^2(x)

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

1 + \frac{1}{2} sin (2)

Decimal

1.45464 \dots

Solution steps

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

Rewrite using trig identities

= \int_{- 1}^{1} \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_{- 1}^{1} 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_{- 1}^{1} 1 d x + \int_{- 1}^{1} cos (2 x) d x)

\int_{- 1}^{1} 1 d x = 2

\int_{- 1}^{1} cos (2 x) d x = sin (2)

= \frac{1}{2} (2 + sin (2))

Simplify

\frac{1}{2} (2 + sin (2)) : 1 + \frac{1}{2} sin (2)

= 1 + \frac{1}{2} sin (2)

\int_{6}^{\infty} \frac{2}{x ^{3}} d x

\int_{3}^{1} \frac{1}{x ^{2} + 1} d x

\int_{0}^{5} x^{2} - x d x

\int_{0}^{3} \frac{x e ^{x^{2}}}{3} d x

\int_{- 1}^{0} e^{- x} - e^{x} d x

What is the integral from-1 to 1 of cos^2(x) ?
The integral from-1 to 1 of cos^2(x) is 1+1/2 sin(2)