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

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

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

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

23

Decimal Notation

3.46410 \dots

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= 2 [tan (x)]_{0}^{\frac{π}{3}}

Compute the boundaries:

3

= 23

y = \frac{7}{x}, (4, \frac{7}{2})

\frac{d}{d x} (50 - x^{2} - x)

x \to \frac{π}{2} lim (tan (x))

\frac{d}{d x} (64)

x = 10 y - y^{2}, x = y^{2} - 4 y

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