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 -sqrt(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

Take the constant out:

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

= - \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}}

Compute the boundaries:

2

= - 2

\int_{1}^{5} \frac{1}{x ^{3}} d x

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

\int_{1}^{5} x^{2} - 2 x - 8 d x

\int_{0}^{4} cos (x) d x

\int_{1}^{1} tan (t) d t

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 -sqrt(2)