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

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

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

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

\frac{π}{2} + 1

Decimal

2.57079 \dots

Solution steps

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

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

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

= \frac{π}{2} + 1

\int_{- 1}^{2} x + ∣ x ∣ d x

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

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

\int_{0}^{1} x^{4} e^{x^{5}} d x

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