What is the integral from (-pi)/4 to pi/4 of cos(x) ?

The integral from (-pi)/4 to pi/4 of cos(x) is square root of 2

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integral from (-pi)/4 to pi/4 of cos(x)

\int_{\frac{- π}{4}}^{\frac{π}{4}} cos (x) d x

2

Decimal Notation

1.41421 \dots

Solution steps

\int_{\frac{- π}{4}}^{\frac{π}{4}} cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= [sin (x)]_{\frac{- π}{4}}^{\frac{π}{4}}

Simplify

= [sin (x)]_{- \frac{π}{4}}^{\frac{π}{4}}

Compute the boundaries:

2

= 2

\int_{0}^{\frac{π}{4}} tan^{3} (θ) d θ

\int_{0}^{2} 15 e^{3 x} d x

\int_{0}^{π} - sin (\frac{n x}{2}) d x

\int_{1}^{2} \frac{1}{y} d y

\int_{2}^{3} (x^{4} - 3 x + 1) d x

What is the integral from (-pi)/4 to pi/4 of cos(x) ?
The integral from (-pi)/4 to pi/4 of cos(x) is square root of 2