What is the integral from 0 to pi/4 of-cos(x) ?

The integral from 0 to pi/4 of-cos(x) is -1/(sqrt(2))

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integral from 0 to pi/4 of-cos(x)

\int_{0}^{\frac{π}{4}} - cos (x) d x

- \frac{1}{2}

Decimal

- 0.70710 \dots

Solution steps

\int_{0}^{\frac{π}{4}} - cos (x) d x

Take the constant out:

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

= - \int_{0}^{\frac{π}{4}} cos (x) d x

Use the common integral:

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

= - [sin (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

= - \frac{1}{2}

\int_{0}^{y} 2 x d x

\int_{0}^{\frac{1}{3}} x^{2} e^{- 3 x} d x

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

\int_{4.9}^{7.2} 12 x^{2} - 6 x + \frac{4}{x} d x

\int_{- 10}^{4} 40 - 6 x - x^{2} d x

What is the integral from 0 to pi/4 of-cos(x) ?
The integral from 0 to pi/4 of-cos(x) is -1/(sqrt(2))