What is the integral from pi/2 to 0 of cos(x) ?

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

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integral from pi/2 to 0 of cos(x)

\int_{\frac{π}{2}}^{0} cos (x) d x

- 1

Solution steps

\int_{\frac{π}{2}}^{0} cos (x) d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{\frac{π}{2}} cos (x) d x

Use the common integral:

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

= - [sin (x)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= - 1

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

\int_{0}^{1} \frac{3}{2 x ^{2} + 5 x + 2} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos^{4} (x) d x

\int_{0}^{3} \frac{x}{x + 1} d x

\int_{0}^{π} ∣ sin (x) ∣ d x

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