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

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

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

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

1

Solution steps

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

Rewrite using trig identities

= \int_{0}^{\frac{π}{2}} sin (x) d x

Use the common integral:

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

= [- cos (x)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= 1

\int_{- 2}^{1} - x^{2} + 9 d x

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

\int_{- 1}^{4} (3 x + 4 - x^{2}) d x

\int_{1}^{4} x - 3 ln (x) - \frac{2}{x} d x

\int_{4}^{10} \frac{x}{4} - \frac{4}{x} d x

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