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

The integral from pi/3 to pi of cos(x+pi/3) is -sqrt(3)

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

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

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int cos (u) d u = sin (u)

= [sin (u)]_{\frac{2 π}{3}}^{π + \frac{π}{3}}

Compute the boundaries:

- 3

= - 3

\int_{0}^{1} 17 x^{3} 1 - x^{2} d x

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

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

\int_{1}^{\infty} x^{p} d x

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

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