What is the integral from pi/4 to (3pi)/4 of cot(x) ?

The integral from pi/4 to (3pi)/4 of cot(x) is 0

Popular >

integral from pi/4 to (3pi)/4 of cot(x)

\int_{\frac{π}{4}}^{\frac{3 π}{4}} cot (x) d x

0

Solution steps

\int_{\frac{π}{4}}^{\frac{3 π}{4}} cot (x) d x

Rewrite using trig identities

= \int_{\frac{π}{4}}^{\frac{3 π}{4}} cos (x) csc (x) d x

Apply Integration By Parts

: [- \int - x csc^{2} (x) d x + x cot (x)]_{\frac{π}{4}}^{\frac{3 π}{4}}

= [- \int - x csc^{2} (x) d x + x cot (x)]_{\frac{π}{4}}^{\frac{3 π}{4}}

\int - x csc^{2} (x) d x = x cot (x) - ln ∣ sin (x) ∣

= [- (x cot (x) - ln ∣ sin (x) ∣) + x cot (x)]_{\frac{π}{4}}^{\frac{3 π}{4}}

Simplify

= [ln ∣ sin (x) ∣]_{\frac{π}{4}}^{\frac{3 π}{4}}

Compute the boundaries:

0

= 0

\int_{π}^{2 π} 5 sin (2 x) d x

\int_{0}^{4} 3 x d x

\int_{- 1}^{1} ∣ x ∣ - x^{2} d x

\int_{0}^{1} x 7 x^{2} + 9 d x

\int_{0}^{4} \frac{1}{4 t ^{2} + 9} d t

What is the integral from pi/4 to (3pi)/4 of cot(x) ?
The integral from pi/4 to (3pi)/4 of cot(x) is 0