What is the integral from 0 to pi/3 of (sec(x))^2 ?

The integral from 0 to pi/3 of (sec(x))^2 is square root of 3

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integral from 0 to pi/3 of (sec(x))^2

\int_{0}^{\frac{π}{3}} (sec (x))^{2} d x

3

Decimal

1.73205 \dots

Solution steps

\int_{0}^{\frac{π}{3}} (sec (x))^{2} d x

Simplify

= \int_{0}^{\frac{π}{3}} sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= [tan (x)]_{0}^{\frac{π}{3}}

Compute the boundaries:

3

= 3

\int_{0}^{1} \frac{x}{( x + 1 ) ^{4}} d x

\int_{0}^{4} sin (\frac{nπ x}{4}) d x

\int_{0}^{3} 12 d x

\int_{1}^{4} 119 x^{\frac{5}{2}} d x

\int_{2}^{3} e^{x^{3}} x^{2} d x

What is the integral from 0 to pi/3 of (sec(x))^2 ?
The integral from 0 to pi/3 of (sec(x))^2 is square root of 3