What is the integral from pi/3 to pi/2 of (x+cos(x)) ?

The integral from pi/3 to pi/2 of (x+cos(x)) is (5pi^2}{72}+1-\frac{sqrt(3))/2

Popular >

integral from pi/3 to pi/2 of (x+cos(x))

\int_{\frac{π}{3}}^{\frac{π}{2}} (x + cos (x)) d x

\frac{5 π ^{2}}{72} + 1 - \frac{3}{2}

Decimal Notation

0.81936 \dots

Solution steps

\int_{\frac{π}{3}}^{\frac{π}{2}} x + 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_{\frac{π}{3}}^{\frac{π}{2}} x d x + \int_{\frac{π}{3}}^{\frac{π}{2}} cos (x) d x

\int_{\frac{π}{3}}^{\frac{π}{2}} x d x = \frac{5 π ^{2}}{72}

\int_{\frac{π}{3}}^{\frac{π}{2}} cos (x) d x = 1 - \frac{3}{2}

= \frac{5 π ^{2}}{72} + 1 - \frac{3}{2}

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

\int_{- 2}^{2} (10 x^{9} + 25 x^{21}) d x

\int_{0}^{4} 25 - x^{2} d x

\int_{- 1}^{2} 3 d x

\int_{0}^{x} e^{2 t} d t

What is the integral from pi/3 to pi/2 of (x+cos(x)) ?
The integral from pi/3 to pi/2 of (x+cos(x)) is (5pi^2}{72}+1-\frac{sqrt(3))/2