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

The integral from pi/4 to (3pi)/4 of csc(x) is ln(sqrt(2)+1)-ln(sqrt(2)-1)

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

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

ln (2 + 1) - ln (2 - 1)

Decimal

1.76274 \dots

Solution steps

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

Apply u-substitution

: \int_{2 - 1}^{2 + 1} \frac{1}{u} d u

= \int_{2 - 1}^{2 + 1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2 - 1}^{2 + 1}

Compute the boundaries:

ln (2 + 1) - ln (2 - 1)

= ln (2 + 1) - ln (2 - 1)

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

\int_{- \frac{π}{6}}^{\frac{π}{6}} tan^{3} (x) d x

\int_{- π}^{0} (π + x) d x

\int_{- 1}^{1} (8 - ∣ x ∣) d x

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

What is the integral from pi/4 to (3pi)/4 of csc(x) ?
The integral from pi/4 to (3pi)/4 of csc(x) is ln(sqrt(2)+1)-ln(sqrt(2)-1)