What is the integral from 0 to pi/4 of (2cos(x)+1) ?

The integral from 0 to pi/4 of (2cos(x)+1) is sqrt(2)+pi/4

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integral from 0 to pi/4 of (2cos(x)+1)

\int_{0}^{\frac{π}{4}} (2 cos (x) + 1) d x

2 + \frac{π}{4}

Decimal

2.19961 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 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}{4}} 2 cos (x) d x + \int_{0}^{\frac{π}{4}} 1 d x

\int_{0}^{\frac{π}{4}} 2 cos (x) d x = 2

\int_{0}^{\frac{π}{4}} 1 d x = \frac{π}{4}

= 2 + \frac{π}{4}

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

\int_{0}^{\frac{π}{2}} sinh (2 x) d x

\int_{- 2}^{0} x^{2} - 4 x d x

\int_{0}^{1} x e^{x} - x d x

\int_{1}^{0} e^{x^{2} - x} d x

What is the integral from 0 to pi/4 of (2cos(x)+1) ?
The integral from 0 to pi/4 of (2cos(x)+1) is sqrt(2)+pi/4