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

\int_{- 2}^{5} \frac{2}{3} d x

\int_{0}^{2 π} \frac{128}{15} d θ

\int_{3}^{7} 2 x d x

\int_{1}^{1.5} (2 x + \frac{3}{2 x ^{2}}) d x

\int_{1}^{5} (x + 1) (x^{2} + 2 x)^{2} d x

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)