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

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

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integral from 0 to pi/2 of cos(x)+1

\int_{0}^{\frac{π}{2}} cos (x) + 1 d x

1 + \frac{π}{2}

Decimal

2.57079 \dots

Solution steps

\int_{0}^{\frac{π}{2}} cos (x) + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{2}} cos (x) d x + \int_{0}^{\frac{π}{2}} 1 d x

\int_{0}^{\frac{π}{2}} cos (x) d x = 1

\int_{0}^{\frac{π}{2}} 1 d x = \frac{π}{2}

= 1 + \frac{π}{2}

\int_{1}^{2} (z + \frac{2}{z}) \cdot (z - \frac{2}{z}) d z

\int_{0}^{1} x 35 x^{2} + 1 d x

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

\int_{0}^{9} \frac{x}{36 + 5 x} d x

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

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