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

The integral from 0 to pi/2 of sin(x+pi/2) is 1

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integral from 0 to pi/2 of sin(x+pi/2)

\int_{0}^{\frac{π}{2}} sin (x + \frac{π}{2}) d x

1

Solution steps

\int_{0}^{\frac{π}{2}} sin (x + \frac{π}{2}) d x

Rewrite using trig identities

= \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_{0}^{1} 0.2 + c x d x

\int_{2}^{3} 95 + 300 t^{2} - 10 t d t

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

\int_{- 2}^{0} 9 x^{2} (2 x^{3} + 2)^{2} d x

\int_{4}^{\infty} \frac{1}{x ^{2} - 9} d x

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