What is the integral from pi/4 to (5pi)/4 of cos(x) ?

The integral from pi/4 to (5pi)/4 of cos(x) is -sqrt(2)

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integral from pi/4 to (5pi)/4 of cos(x)

\int_{\frac{π}{4}}^{\frac{5 π}{4}} cos (x) d x

- 2

Decimal

- 1.41421 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{5 π}{4}} cos (x) d x

Use the common integral:

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

= [sin (x)]_{\frac{π}{4}}^{\frac{5 π}{4}}

Compute the boundaries:

- 2

= - 2

What is the integral from pi/4 to (5pi)/4 of cos(x) ?
The integral from pi/4 to (5pi)/4 of cos(x) is -sqrt(2)