What is the integral from pi/3 to x of csc^2(t) ?

The integral from pi/3 to x of csc^2(t) is -cot(x)+1/(sqrt(3))

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integral from pi/3 to x of csc^2(t)

\int_{\frac{π}{3}}^{x} csc^{2} (t) d t

- cot (x) + \frac{1}{3}

Solution steps

\int_{\frac{π}{3}}^{x} csc^{2} (t) d t

Use the common integral:

\int csc^{2} (t) d t = - cot (t)

= [- cot (t)]_{\frac{π}{3}}^{x}

Compute the boundaries:

- cot (x) + \frac{1}{3}

= - cot (x) + \frac{1}{3}

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

\int_{- 1}^{2} x^{2} - 4 x + 3 d x

\int_{- y}^{y} \frac{1}{4} (y - x) e^{- y} d x

\int_{- π}^{π} sin^{2} (3 x) d x

\int_{π}^{π} x sin (x) d x

What is the integral from pi/3 to x of csc^2(t) ?
The integral from pi/3 to x of csc^2(t) is -cot(x)+1/(sqrt(3))